Factors of an integer
You are encouraged to solve this task according to the task description, using any language you may know.
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- Task
Compute the factors of a positive integer.
These factors are the positive integers by which the number being factored can be divided to yield a positive integer result.
(Though the concepts function correctly for zero and negative integers, the set of factors of zero has countably infinite members, and the factors of negative integers can be obtained from the factors of related positive numbers without difficulty; this task does not require handling of either of these cases).
Note that every prime number has two factors: 1 and itself.
- Related tasks
- count in factors
- prime decomposition
- Sieve of Eratosthenes
- primality by trial division
- factors of a Mersenne number
- trial factoring of a Mersenne number
- partition an integer X into N primes
- sequence of primes by Trial Division
- sequence: smallest number greater than previous term with exactly n divisors
0815
<:1:~>|~#:end:>~x}:str:/={^:wei:~%x<:a:x=$~
=}:wei:x<:1:+{>~>x=-#:fin:^:str:}:fin:{{~%11l
F factor(n)
V factors = Set[Int]()
L(x) 1..Int(sqrt(n))
I n % x == 0
factors.add(x)
factors.add(n I/ x)
R sorted(Array(factors))
L(i) (45, 53, 64)
print(i‘: factors: ’String(factor(i)))- Output:
45: factors: [1, 3, 5, 9, 15, 45] 53: factors: [1, 53] 64: factors: [1, 2, 4, 8, 16, 32, 64]
360 Assembly
Very compact version.
* Factors of an integer - 07/10/2015
FACTOR CSECT
USING FACTOR,R15 set base register
LA R7,PG pgi=@pg
LA R6,1 i
L R3,N loop count
LOOP L R5,N n
LA R4,0
DR R4,R6 n/i
LTR R4,R4 if mod(n,i)=0
BNZ NEXT
XDECO R6,PG+120 edit i
MVC 0(6,R7),PG+126 output i
LA R7,6(R7) pgi=pgi+6
NEXT LA R6,1(R6) i=i+1
BCT R3,LOOP loop
XPRNT PG,120 print buffer
XR R15,R15 set return code
BR R14 return to caller
N DC F'12345' <== input value
PG DC CL132' ' buffer
YREGS
END FACTOR- Output:
1 3 5 15 823 2469 4115 12345
68000 Assembly
;max input range equals 0 to 0xFFFFFFFF.
jsr GetInput ;unimplemented routine to get user input for a positive (nonzero) integer.
;output of this routine will be in D0.
MOVE.L D0,D1 ;D1 will be used for temp storage.
MOVE.L #1,D2 ;start with 1.
computeFactors:
DIVU D2,D1 ;remainder is in top 2 bytes, quotient in bottom 2.
MOVE.L D1,D3 ;temporarily store into D3 to check the remainder
SWAP D3 ;swap the high and low words of D3. Now bottom 2 bytes contain remainder.
CMP.W #0,D3 ;is the bottom word equal to 0?
BNE D2_Wasnt_A_Divisor ;if not, D2 was not a factor of D1.
JSR PrintD2 ;unimplemented routine to print D2 to the screen as a decimal number.
D2_Wasnt_A_Divisor:
MOVE.L D0,D1 ;restore D1.
ADDQ.L #1,D2 ;increment D2
CMP.L D2,D1 ;is D2 now greater than D1?
BLS computeFactors ;if not, loop again
;end of program
AArch64 Assembly
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program factorst64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
.equ CHARPOS, '@'
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessDeb: .ascii "Factors of : @ are : \n"
szMessFactor: .asciz "@ \n"
szCarriageReturn: .asciz "\n"
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
sZoneConversion: .skip 100
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main: // entry of program
mov x0,#100
bl factors
mov x0,#97
bl factors
ldr x0,qNumber
bl factors
100: // standard end of the program
mov x0, #0 // return code
mov x8, #EXIT // request to exit program
svc 0 // perform the system call
qNumber: .quad 32767
qAdrszCarriageReturn: .quad szCarriageReturn
/******************************************************************/
/* calcul factors of number */
/******************************************************************/
/* x0 contains the number to factorize */
factors:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
mov x5,x0 // limit calcul
ldr x1,qAdrsZoneConversion // conversion register in decimal string
bl conversion10S
ldr x0,qAdrszMessDeb // display message
ldr x1,qAdrsZoneConversion
bl strInsertAtChar
bl affichageMess
mov x6,#1 // counter loop
1: // loop
udiv x0,x5,x6 // division
msub x3,x0,x6,x5 // compute remainder
cbnz x3,2f // remainder not = zero -> loop
// display result if yes
mov x0,x6
ldr x1,qAdrsZoneConversion
bl conversion10S
ldr x0,qAdrszMessFactor // display message
ldr x1,qAdrsZoneConversion
bl strInsertAtChar
bl affichageMess
2:
add x6,x6,#1 // add 1 to loop counter
cmp x6,x5 // <= number ?
ble 1b // yes loop
100:
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret
qAdrszMessDeb: .quad szMessDeb
qAdrszMessFactor: .quad szMessFactor
qAdrsZoneConversion: .quad sZoneConversion
/******************************************************************/
/* insert string at character insertion */
/******************************************************************/
/* x0 contains the address of string 1 */
/* x1 contains the address of insertion string */
/* x0 return the address of new string on the heap */
/* or -1 if error */
strInsertAtChar:
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
stp x5,x6,[sp,-16]! // save registers
stp x7,x8,[sp,-16]! // save registers
mov x3,#0 // length counter
1: // compute length of string 1
ldrb w4,[x0,x3]
cmp w4,#0
cinc x3,x3,ne // increment to one if not equal
bne 1b // loop if not equal
mov x5,#0 // length counter insertion string
2: // compute length to insertion string
ldrb w4,[x1,x5]
cmp x4,#0
cinc x5,x5,ne // increment to one if not equal
bne 2b // and loop
cmp x5,#0
beq 99f // string empty -> error
add x3,x3,x5 // add 2 length
add x3,x3,#1 // +1 for final zero
mov x6,x0 // save address string 1
mov x0,#0 // allocation place heap
mov x8,BRK // call system 'brk'
svc #0
mov x5,x0 // save address heap for output string
add x0,x0,x3 // reservation place x3 length
mov x8,BRK // call system 'brk'
svc #0
cmp x0,#-1 // allocation error
beq 99f
mov x2,0
mov x4,0
3: // loop copy string begin
ldrb w3,[x6,x2]
cmp w3,0
beq 99f
cmp w3,CHARPOS // insertion character ?
beq 5f // yes
strb w3,[x5,x4] // no store character in output string
add x2,x2,1
add x4,x4,1
b 3b // and loop
5: // x4 contains position insertion
add x8,x4,1 // init index character output string
// at position insertion + one
mov x3,#0 // index load characters insertion string
6:
ldrb w0,[x1,x3] // load characters insertion string
cmp w0,#0 // end string ?
beq 7f // yes
strb w0,[x5,x4] // store in output string
add x3,x3,#1 // increment index
add x4,x4,#1 // increment output index
b 6b // and loop
7: // loop copy end string
ldrb w0,[x6,x8] // load other character string 1
strb w0,[x5,x4] // store in output string
cmp x0,#0 // end string 1 ?
beq 8f // yes -> end
add x4,x4,#1 // increment output index
add x8,x8,#1 // increment index
b 7b // and loop
8:
mov x0,x5 // return output string address
b 100f
99: // error
mov x0,#-1
100:
ldp x7,x8,[sp],16 // restaur 2 registers
ldp x5,x6,[sp],16 // restaur 2 registers
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"ACL2
(defun factors-r (n i)
(declare (xargs :measure (nfix (- n i))))
(cond ((zp (- n i))
(list n))
((= (mod n i) 0)
(cons i (factors-r n (1+ i))))
(t (factors-r n (1+ i)))))
(defun factors (n)
(factors-r n 1))
Action!
PROC PrintFactors(CARD a)
BYTE notFirst
CARD p
p=1 notFirst=0
WHILE p<=a
DO
IF a MOD p=0 THEN
IF notFirst THEN
Print(", ")
FI
notFirst=1
PrintC(p)
FI
p==+1
OD
RETURN
PROC Test(CARD a)
PrintF("Factors of %U: ",a)
PrintFactors(a)
PutE()
RETURN
PROC Main()
Test(1)
Test(101)
Test(666)
Test(1977)
Test(2021)
Test(6502)
Test(12345)
RETURN- Output:
Screenshot from Atari 8-bit computer
Factors of 1: 1 Factors of 101: 1, 101 Factors of 666: 1, 2, 3, 6, 9, 18, 37,74, 111, 222, 333, 666 Factors of 1977: 1, 3, 659, 1977 Factors of 2021: 1, 43, 47, 2021 Factors of 6502: 1, 2, 3251, 6502 Factors of 12345: 1, 3, 5, 15, 823, 2469, 4115, 12345
ActionScript
function factor(n:uint):Vector.<uint>
{
var factors:Vector.<uint> = new Vector.<uint>();
for(var i:uint = 1; i <= n; i++)
if(n % i == 0)factors.push(i);
return factors;
}
Ada
with Ada.Text_IO;
with Ada.Command_Line;
procedure Factors is
Number : Positive;
Test_Nr : Positive := 1;
begin
if Ada.Command_Line.Argument_Count /= 1 then
Ada.Text_IO.Put (Ada.Text_IO.Standard_Error, "Missing argument!");
Ada.Command_Line.Set_Exit_Status (Ada.Command_Line.Failure);
return;
end if;
Number := Positive'Value (Ada.Command_Line.Argument (1));
Ada.Text_IO.Put ("Factors of" & Positive'Image (Number) & ": ");
loop
if Number mod Test_Nr = 0 then
Ada.Text_IO.Put (Positive'Image (Test_Nr) & ",");
end if;
exit when Test_Nr ** 2 >= Number;
Test_Nr := Test_Nr + 1;
end loop;
Ada.Text_IO.Put_Line (Positive'Image (Number) & ".");
end Factors;
Aikido
import math
function factor (n:int) {
var result = []
function append (v) {
if (!(v in result)) {
result.append (v)
}
}
var sqrt = cast<int>(Math.sqrt (n))
append (1)
for (var i = n-1 ; i >= sqrt ; i--) {
if ((n % i) == 0) {
append (i)
append (n/i)
}
}
append (n)
return result.sort()
}
function printvec (vec) {
var comma = ""
print ("[")
foreach v vec {
print (comma + v)
comma = ", "
}
println ("]")
}
printvec (factor (45))
printvec (factor (25))
printvec (factor (100))ALGOL 68
Note: The following implements generators, eliminating the need of declaring arbitrarily long int arrays for caching.
MODE YIELDINT = PROC(INT)VOID;
PROC gen factors = (INT n, YIELDINT yield)VOID: (
FOR i FROM 1 TO ENTIER sqrt(n) DO
IF n MOD i = 0 THEN
yield(i);
INT other = n OVER i;
IF i NE other THEN yield(n OVER i) FI
FI
OD
);
[]INT nums2factor = (45, 53, 64);
FOR i TO UPB nums2factor DO
INT num = nums2factor[i];
STRING sep := ": ";
print(num);
# FOR INT j IN # gen factors(num, # ) DO ( #
## (INT j)VOID:(
print((sep,whole(j,0)));
sep:=", "
# OD # ));
print(new line)
OD- Output:
+45: 1, 45, 3, 15, 5, 9
+53: 1, 53
+64: 1, 64, 2, 32, 4, 16, 8
ALGOL W
begin
% return the factors of n ( n should be >= 1 ) in the array factor %
% the bounds of factor should be 0 :: len (len must be at least 1) %
% the number of factors will be returned in factor( 0 ) %
procedure getFactorsOf ( integer value n
; integer array factor( * )
; integer value len
) ;
begin
for i := 0 until len do factor( i ) := 0;
if n >= 1 and len >= 1 then begin
integer pos, lastFactor;
factor( 0 ) := factor( 1 ) := pos := 1;
% find the factors up to sqrt( n ) %
for f := 2 until truncate( sqrt( n ) ) + 1 do begin
if ( n rem f ) = 0 and pos <= len then begin
% found another factor and there's room to store it %
pos := pos + 1;
factor( 0 ) := pos;
factor( pos ) := f
end if_found_factor
end for_f;
% find the factors above sqrt( n ) %
lastFactor := factor( factor( 0 ) );
for f := factor( 0 ) step -1 until 1 do begin
integer newFactor;
newFactor := n div factor( f );
if newFactor > lastFactor and pos <= len then begin
% found another factor and there's room to store it %
pos := pos + 1;
factor( 0 ) := pos;
factor( pos ) := newFactor
end if_found_factor
end for_f;
end if_params_ok
end getFactorsOf ;
% prpocedure to test getFactorsOf %
procedure testFactorsOf( integer value n ) ;
begin
integer array factor( 0 :: 100 );
getFactorsOf( n, factor, 100 );
i_w := 1; s_w := 0; % set output format %
write( n, " has ", factor( 0 ), " factors:" );
for f := 1 until factor( 0 ) do writeon( " ", factor( f ) )
end testFactorsOf ;
% test the factorising %
for i := 1 until 100 do testFactorsOf( i )
end.- Output:
1 has 1 factors: 1 2 has 2 factors: 1 2 3 has 2 factors: 1 3 4 has 3 factors: 1 2 4 ... 96 has 12 factors: 1 2 3 4 6 8 12 16 24 32 48 96 97 has 2 factors: 1 97 98 has 6 factors: 1 2 7 14 49 98 99 has 6 factors: 1 3 9 11 33 99 100 has 9 factors: 1 2 4 5 10 20 25 50 100
ALGOL-M
Instead of displaying 1 and the number itself as factors, prime numbers are explicitly reported as such. To reduce the number of test divisions, only odd divisors are tested if an initial check shows the number to be factored is not even. The upper limit of divisors is set at N/2 or N/3, depending on whether N is even or odd, and is continuously reduced to N divided by the next potential divisor until the first factor is found. For a prime number the resulting limit will be the square root of N, which avoids the necessity of explicitly calculating that value. (ALGOL-M does not have a built-in square root function.)
BEGIN
COMMENT RETURN P MOD Q;
INTEGER FUNCTION MOD (P, Q);
INTEGER P, Q;
BEGIN
MOD := P - Q * (P / Q);
END;
INTEGER I, N, LIMIT, FOUND, START, DELTA;
WHILE 1 = 1 DO
BEGIN
WRITE ("NUMBER TO FACTOR (OR 0 TO QUIT):");
READ (N);
IF N = 0 THEN GOTO DONE;
WRITE ("THE FACTORS ARE:");
COMMENT CHECK WHETHER NUMBER IS EVEN OR ODD;
IF MOD(N, 2) = 0 THEN
BEGIN
START := 2;
DELTA := 1;
END
ELSE
BEGIN
START := 3;
DELTA := 2;
END;
COMMENT TEST POTENTIAL DIVISORS;
FOUND := 0;
I := START;
LIMIT := N / I;
WHILE I <= LIMIT DO
BEGIN
IF MOD(N, I) = 0 THEN
BEGIN
WRITEON (I);
FOUND := FOUND + 1;
END;
I := I + DELTA;
IF FOUND = 0 THEN LIMIT := N / I;
END;
IF FOUND = 0 THEN WRITEON (" NONE - THE NUMBER IS PRIME.");
WRITE("");
END;
DONE: WRITE ("GOODBYE");
END- Output:
NUMBER TO FACTOR (OR 0 TO QUIT): -> 96 THE FACTORS ARE: 2 3 4 6 8 12 16 24 32 48 NUMBER TO FACTOR (OR 0 TO QUIT): -> 97 THE FACTORS ARE: NONE - THE NUMBER IS PRIME. NUMBER TO FACTOR (OR 0 TO QUIT): -> 98 THE FACTORS ARE: 2 7 14 49 NUMBER TO FACTOR (OR 0 TO QUIT): -> 0 GOODBYE
APL
factors←{(0=(⍳⍵)|⍵)/⍳⍵}
factors 12345
1 3 5 15 823 2469 4115 12345
factors 720
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720
Apple
> (λn. (λk. n|k=0) #. ⍳ 1 n 1) 60
Vec 12 [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]AppleScript
Functional
-- integerFactors :: Int -> [Int]
on integerFactors(n)
if n = 1 then
{1}
else if 1 > n then
missing value
else
set realRoot to n ^ (1 / 2)
set intRoot to realRoot as integer
set blnPerfectSquare to intRoot = realRoot
-- isFactor :: Int -> Bool
script isFactor
on |λ|(x)
(n mod x) = 0
end |λ|
end script
-- Factors up to square root of n,
set lows to filter(isFactor, enumFromTo(1, intRoot))
-- integerQuotient :: Int -> Int
script integerQuotient
on |λ|(x)
(n / x) as integer
end |λ|
end script
-- and quotients of these factors beyond the square root.
lows & map(integerQuotient, ¬
items (1 + (blnPerfectSquare as integer)) thru -1 of reverse of lows)
end if
end integerFactors
--------------------------- TEST -------------------------
on run
integerFactors(120)
--> {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}
end run
-------------------- GENERIC FUNCTIONS -------------------
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- filter :: (a -> Bool) -> [a] -> [a]
on filter(f, xs)
tell mReturn(f)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
return lst
end tell
end filter
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
- Output:
{1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}
Straightforward
on factors(n)
set output to {}
set sqrt to n ^ 0.5
set limit to sqrt div 1
if (limit = sqrt) then
set end of output to limit
set limit to limit - 1
end if
repeat with i from limit to 1 by -1
if (n mod i is 0) then
set beginning of output to i
set end of output to n div i
end if
end repeat
return output
end factors
factors(123456789)
- Output:
{1, 3, 9, 3607, 3803, 10821, 11409, 32463, 34227, 13717421, 41152263, 123456789}
Arc
(= divisor (fn (num)
(= dlist '())
(when (is 1 num) (= dlist '(1 0)))
(when (is 2 num) (= dlist '(2 1)))
(unless (or (is 1 num) (is 2 num))
(up i 1 (+ 1 (/ num 2))
(if (is 0 (mod num i))
(push i dlist)))
(= dlist (cons num dlist)))
dlist))
(map [rev _] (map [divisor _] '(45 53 60 64)))- Output:
'(
(1 3 5 9 15 45)
(1 53)
(1 2 3 4 5 6 10 12 15 20 30 60)
(1 2 4 8 16 32 64)
)ARM Assembly
/* ARM assembly Raspberry PI */
/* program factorst.s */
/* Constantes */
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
/* Initialized data */
.data
szMessDeb: .ascii "Factors of :"
sMessValeur: .fill 12, 1, ' '
.asciz "are : \n"
sMessFactor: .fill 12, 1, ' '
.asciz "\n"
szCarriageReturn: .asciz "\n"
/* UnInitialized data */
.bss
/* code section */
.text
.global main
main: /* entry of program */
push {fp,lr} /* saves 2 registers */
mov r0,#100
bl factors
mov r0,#97
bl factors
ldr r0,iNumber
bl factors
100: /* standard end of the program */
mov r0, #0 @ return code
pop {fp,lr} @restaur 2 registers
mov r7, #EXIT @ request to exit program
swi 0 @ perform the system call
iNumber: .int 32767
iAdrszCarriageReturn: .int szCarriageReturn
/******************************************************************/
/* calcul factors of number */
/******************************************************************/
/* r0 contains the number */
factors:
push {fp,lr} /* save registres */
push {r1-r6} /* save others registers */
mov r5,r0 @ limit calcul
ldr r1,iAdrsMessValeur @ conversion register in decimal string
bl conversion10S
ldr r0,iAdrszMessDeb @ display message
bl affichageMess
mov r6,#1 @ counter loop
1: @ loop
mov r0,r5 @ dividende
mov r1,r6 @ divisor
bl division
cmp r3,#0 @ remainder = zero ?
bne 2f
@ display result if yes
mov r0,r6
ldr r1,iAdrsMessFactor
bl conversion10S
ldr r0,iAdrsMessFactor
bl affichageMess
2:
add r6,#1 @ add 1 to loop counter
cmp r6,r5 @ <= number ?
ble 1b @ yes loop
100:
pop {r1-r6} /* restaur others registers */
pop {fp,lr} /* restaur des 2 registres */
bx lr /* return */
iAdrsMessValeur: .int sMessValeur
iAdrszMessDeb: .int szMessDeb
iAdrsMessFactor: .int sMessFactor
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {fp,lr} /* save registres */
push {r0,r1,r2,r7} /* save others registers */
mov r2,#0 /* counter length */
1: /* loop length calculation */
ldrb r1,[r0,r2] /* read octet start position + index */
cmp r1,#0 /* if 0 its over */
addne r2,r2,#1 /* else add 1 in the length */
bne 1b /* and loop */
/* so here r2 contains the length of the message */
mov r1,r0 /* address message in r1 */
mov r0,#STDOUT /* code to write to the standard output Linux */
mov r7, #WRITE /* code call system "write" */
swi #0 /* call systeme */
pop {r0,r1,r2,r7} /* restaur others registers */
pop {fp,lr} /* restaur des 2 registres */
bx lr /* return */
/*=============================================*/
/* division integer unsigned */
/*============================================*/
division:
/* r0 contains N */
/* r1 contains D */
/* r2 contains Q */
/* r3 contains R */
push {r4, lr}
mov r2, #0 /* r2 ? 0 */
mov r3, #0 /* r3 ? 0 */
mov r4, #32 /* r4 ? 32 */
b 2f
1:
movs r0, r0, LSL #1 /* r0 ? r0 << 1 updating cpsr (sets C if 31st bit of r0 was 1) */
adc r3, r3, r3 /* r3 ? r3 + r3 + C. This is equivalent to r3 ? (r3 << 1) + C */
cmp r3, r1 /* compute r3 - r1 and update cpsr */
subhs r3, r3, r1 /* if r3 >= r1 (C=1) then r3 ? r3 - r1 */
adc r2, r2, r2 /* r2 ? r2 + r2 + C. This is equivalent to r2 ? (r2 << 1) + C */
2:
subs r4, r4, #1 /* r4 ? r4 - 1 */
bpl 1b /* if r4 >= 0 (N=0) then branch to .Lloop1 */
pop {r4, lr}
bx lr
/***************************************************/
/* conversion register in string décimal signed */
/***************************************************/
/* r0 contains the register */
/* r1 contains address of conversion area */
conversion10S:
push {fp,lr} /* save registers frame and return */
push {r0-r5} /* save other registers */
mov r2,r1 /* early storage area */
mov r5,#'+' /* default sign is + */
cmp r0,#0 /* négatif number ? */
movlt r5,#'-' /* yes sign is - */
mvnlt r0,r0 /* and inverse in positive value */
addlt r0,#1
mov r4,#10 /* area length */
1: /* conversion loop */
bl divisionpar10 /* division */
add r1,#48 /* add 48 at remainder for conversion ascii */
strb r1,[r2,r4] /* store byte area r5 + position r4 */
sub r4,r4,#1 /* previous position */
cmp r0,#0
bne 1b /* loop if quotient not equal zéro */
strb r5,[r2,r4] /* store sign at current position */
subs r4,r4,#1 /* previous position */
blt 100f /* if r4 < 0 end */
/* else complete area with space */
mov r3,#' ' /* character space */
2:
strb r3,[r2,r4] /* store byte */
subs r4,r4,#1 /* previous position */
bge 2b /* loop if r4 greather or equal zero */
100: /* standard end of function */
pop {r0-r5} /*restaur others registers */
pop {fp,lr} /* restaur des 2 registers frame et return */
bx lr
/***************************************************/
/* division par 10 signé */
/* Thanks to http://thinkingeek.com/arm-assembler-raspberry-pi/*
/* and http://www.hackersdelight.org/ */
/***************************************************/
/* r0 contient le dividende */
/* r0 retourne le quotient */
/* r1 retourne le reste */
divisionpar10:
/* r0 contains the argument to be divided by 10 */
push {r2-r4} /* save autres registres */
mov r4,r0
ldr r3, .Ls_magic_number_10 /* r1 <- magic_number */
smull r1, r2, r3, r0 /* r1 <- Lower32Bits(r1*r0). r2 <- Upper32Bits(r1*r0) */
mov r2, r2, ASR #2 /* r2 <- r2 >> 2 */
mov r1, r0, LSR #31 /* r1 <- r0 >> 31 */
add r0, r2, r1 /* r0 <- r2 + r1 */
add r2,r0,r0, lsl #2 /* r2 <- r0 * 5 */
sub r1,r4,r2, lsl #1 /* r1 <- r4 - (r2 * 2) = r4 - (r0 * 10) */
pop {r2-r4}
bx lr /* leave function */
.align 4
.Ls_magic_number_10: .word 0x66666667Arturo
factors: $[num][
select 1..num [x][
(num%x)=0
]
]
print factors 36
- Output:
1 2 3 4 6 9 12 18 36
Asymptote
int[] n = {11, 21, 32, 45, 67, 519};
for(var j : n) {
write(j, suffix=none);
write(" =>", suffix=none);
for(int i = 1; i < (j/2); ++i) {
if(j % i == 0) {
write(" ", i, suffix=none);
}
}
write(" ", j);
}
- Output:
11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 32 45 => 1 3 5 9 15 45 67 => 1 67 519 => 1 3 173 519
AutoHotkey
msgbox, % factors(45) "`n" factors(53) "`n" factors(64)
Factors(n)
{ Loop, % floor(sqrt(n))
{ v := A_Index = 1 ? 1 "," n : mod(n,A_Index) ? v : v "," A_Index "," n//A_Index
}
Sort, v, N U D,
Return, v
}
- Output:
1,3,5,9,15,45 1,53 1,2,4,8,16,32,64
AutoIt
;AutoIt Version: 3.2.10.0
$num = 45
MsgBox (0,"Factors", "Factors of " & $num & " are: " & factors($num))
consolewrite ("Factors of " & $num & " are: " & factors($num))
Func factors($intg)
$ls_factors=""
For $i = 1 to $intg/2
if ($intg/$i - int($intg/$i))=0 Then
$ls_factors=$ls_factors&$i &", "
EndIf
Next
Return $ls_factors&$intg
EndFunc
- Output:
Factors of 45 are: 1, 3, 5, 9, 15, 45
AWK
# syntax: GAWK -f FACTORS_OF_AN_INTEGER.AWK
BEGIN {
print("enter a number or C/R to exit")
}
{ if ($0 == "") { exit(0) }
if ($0 !~ /^[0-9]+$/) {
printf("invalid: %s\n",$0)
next
}
n = $0
printf("factors of %s:",n)
for (i=1; i<=n; i++) {
if (n % i == 0) {
printf(" %d",i)
}
}
printf("\n")
}
- Output:
enter a number or C/R to exit invalid: -1 factors of 0: factors of 1: 1 factors of 2: 1 2 factors of 11: 1 11 factors of 64: 1 2 4 8 16 32 64 factors of 100: 1 2 4 5 10 20 25 50 100 factors of 32766: 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766 factors of 32767: 1 7 31 151 217 1057 4681 32767
BASIC
Applesoft BASIC
The Factors_of_an_integer#Sinclair ZX81 BASIC code works the same in Applesoft BASIC.
ASIC
REM Factors of an integer
PRINT "Enter an integer";
LOOP:
INPUT N
IF N = 0 THEN LOOP:
NA = ABS(N)
NDIV2 = NA / 2
FOR I = 1 TO NDIV2
NMODI = NA MOD I
IF NMODI = 0 THEN
PRINT I;
ENDIF
NEXT I
PRINT NA
END
- Output:
Enter an integer?60
1 2 3 4 5 6 10 12 15 20 30 60
BASIC256
subroutine printFactors(n)
print n; " => ";
for i = 1 to n / 2
if n mod i = 0 then print i; " ";
next i
print n
end subroutine
call printFactors(11)
call printFactors(21)
call printFactors(32)
call printFactors(45)
call printFactors(67)
call printFactors(96)
endBBC BASIC
INSTALL @lib$+"SORTLIB"
sort% = FN_sortinit(0, 0)
PRINT "The factors of 45 are " FNfactorlist(45)
PRINT "The factors of 12345 are " FNfactorlist(12345)
END
DEF FNfactorlist(N%)
LOCAL C%, I%, L%(), L$
DIM L%(32)
FOR I% = 1 TO SQR(N%)
IF (N% MOD I% = 0) THEN
L%(C%) = I%
C% += 1
IF (N% <> I%^2) THEN
L%(C%) = (N% DIV I%)
C% += 1
ENDIF
ENDIF
NEXT I%
CALL sort%, L%(0)
FOR I% = 0 TO C%-1
L$ += STR$(L%(I%)) + ", "
NEXT
= LEFT$(LEFT$(L$))
- Output:
The factors of 45 are 1, 3, 5, 9, 15, 45 The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345
Chipmunk Basic
10 cls
20 printfactors(11)
30 printfactors(21)
40 printfactors(32)
50 printfactors(45)
60 printfactors(67)
70 printfactors(96)
80 end
100 sub printfactors(n)
110 if n < 1 then printfactors = 0
120 print n "=> ";
130 for i = 1 to n/2
140 if n mod i = 0 then print i " ";
150 next i
160 print n
170 end sub
Craft Basic
do
input "enter an integer", n
loop n = 0
let a = abs(n)
for i = 1 to int(a / 2)
if a = int(a / i) * i then
print i
endif
next i
print a
- Output:
?60 1 2 3 4 5 6 10 12 15 20 30 60
FreeBASIC
' FB 1.05.0 Win64
Sub printFactors(n As Integer)
If n < 1 Then Return
Print n; " =>";
For i As Integer = 1 To n / 2
If n Mod i = 0 Then Print i; " ";
Next i
Print n
End Sub
printFactors(11)
printFactors(21)
printFactors(32)
printFactors(45)
printFactors(67)
printFactors(96)
Print
Print "Press any key to quit"
Sleep
- Output:
11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 16 32 45 => 1 3 5 9 15 45 67 => 1 67 96 => 1 2 3 4 6 8 12 16 24 32 48 96
FutureBasic
window 1, @"Factors of an Integer", (0,0,1000,270)
clear local mode
local fn IntegerFactors( f as long ) as CFStringRef
long i, s, l(100), c = 0
CFStringRef factorStr = @""
for i = 1 to sqr(f)
if ( f mod i == 0 )
l(c) = i
c++
if ( f != i ^ 2 )
l(c) = ( f / i )
c++
end if
end if
next i
s = 1
while ( s = 1 )
s = 0
for i = 0 to c-1
if l(i) > l(i+1) and l(i+1) != 0
swap l(i), l(i+1)
s = 1
end if
next i
wend
for i = 0 to c - 1
if ( i < c - 1 )
factorStr = fn StringWithFormat( @"%@ %ld, ", factorStr, l(i) )
else
factorStr = fn StringWithFormat( @"%@ %ld", factorStr, l(i) )
end if
next
end fn = factorStr
print @"Factors of 25 are:"; fn IntegerFactors( 25 )
print @"Factors of 45 are:"; fn IntegerFactors( 45 )
print @"Factors of 103 are:"; fn IntegerFactors( 103 )
print @"Factors of 760 are:"; fn IntegerFactors( 760 )
print @"Factors of 12345 are:"; fn IntegerFactors( 12345 )
print @"Factors of 32766 are:"; fn IntegerFactors( 32766 )
print @"Factors of 32767 are:"; fn IntegerFactors( 32767 )
print @"Factors of 57097 are:"; fn IntegerFactors( 57097 )
print @"Factors of 12345678 are:"; fn IntegerFactors( 12345678 )
print @"Factors of 32434243 are:"; fn IntegerFactors( 32434243 )
HandleEvents- Output:
Factors of 25 are: 1, 5, 25 Factors of 45 are: 1, 3, 5, 9, 15, 45 Factors of 103 are: 1, 103 Factors of 760 are: 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760 Factors of 12345 are: 1, 3, 5, 15, 823, 2469, 4115, 12345 Factors of 32766 are: 1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766 Factors of 32767 are: 1, 7, 31, 151, 217, 1057, 4681, 32767 Factors of 57097 are: 1, 57097 Factors of 12345678 are: 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 14593, 29186, 43779, 87558, 131337, 262674, 685871, 1371742, 2057613, 4115226, 6172839, 12345678 Factors of 32434243 are: 1, 307, 105649, 32434243
Gambas
Public Sub Main()
printFactors(11)
printFactors(21)
printFactors(32)
printFactors(45)
printFactors(67)
printFactors(96)
End
Sub printFactors(n As Integer)
If n < 1 Then Return
Print n; " =>";
For i As Integer = 1 To n / 2
If n Mod i = 0 Then Print i; " ";
Next
Print n
End Sub
GW-BASIC
10 INPUT "Enter an integer: ", N
20 IF N = 0 THEN GOTO 10
30 NA = ABS(N)
40 FOR I = 1 TO NA/2
50 IF NA MOD I = 0 THEN PRINT I;
60 NEXT I
70 PRINT NA
- Output:
Enter an integer: 1 1 Enter an integer: 12 1 2 3 4 6 12 Enter an integer: 13 1 13 Enter an integer: -22222 1 2 41 82 271 542 11111 22222
IS-BASIC
100 PROGRAM "Factors.bas"
110 INPUT PROMPT "Number: ":N
120 FOR I=1 TO INT(N/2)
130 IF MOD(N,I)=0 THEN PRINT I;
140 NEXT
150 PRINT N
Liberty BASIC
num = 10677106534462215678539721403561279
maxnFactors = 1000
dim primeFactors(maxnFactors), nPrimeFactors(maxnFactors)
global nDifferentPrimeNumbersFound, nFactors, iFactor
print "Start finding all factors of ";num; ":"
nDifferentPrimeNumbersFound=0
dummy = factorize(num,2)
nFactors = showPrimeFactors(num)
dim factors(nFactors)
dummy = generateFactors(1,1)
sort factors(), 0, nFactors-1
for i=1 to nFactors
print i;" ";factors(i-1)
next i
print "done"
wait
function factorize(iNum,offset)
factorFound=0
i = offset
do
if (iNum MOD i)=0 _
then
if primeFactors(nDifferentPrimeNumbersFound) = i _
then
nPrimeFactors(nDifferentPrimeNumbersFound) = nPrimeFactors(nDifferentPrimeNumbersFound) + 1
else
nDifferentPrimeNumbersFound = nDifferentPrimeNumbersFound + 1
primeFactors(nDifferentPrimeNumbersFound) = i
nPrimeFactors(nDifferentPrimeNumbersFound) = 1
end if
if iNum/i<>1 then dummy = factorize(iNum/i,i)
factorFound=1
end if
i=i+1
loop while factorFound=0 and i<=sqr(iNum)
if factorFound=0 _
then
nDifferentPrimeNumbersFound = nDifferentPrimeNumbersFound + 1
primeFactors(nDifferentPrimeNumbersFound) = iNum
nPrimeFactors(nDifferentPrimeNumbersFound) = 1
end if
end function
function showPrimeFactors(iNum)
showPrimeFactors=1
print iNum;" = ";
for i=1 to nDifferentPrimeNumbersFound
print primeFactors(i);"^";nPrimeFactors(i);
if i<nDifferentPrimeNumbersFound then print " * "; else print ""
showPrimeFactors = showPrimeFactors*(nPrimeFactors(i)+1)
next i
end function
function generateFactors(product,pIndex)
if pIndex>nDifferentPrimeNumbersFound _
then
factors(iFactor) = product
iFactor=iFactor+1
else
for i=0 to nPrimeFactors(pIndex)
dummy = generateFactors(product*primeFactors(pIndex)^i,pIndex+1)
next i
end if
end function- Output:
Start finding all factors of 10677106534462215678539721403561279:
10677106534462215678539721403561279 = 29269^1 * 32579^1 * 98731^2 * 104729^3
1 1
2 29269
3 32579
4 98731
5 104729
6 953554751
7 2889757639
8 3065313101
9 3216557249
10 3411966091
11 9747810361
12 10339998899
13 10968163441
14 94145414120981
15 99864835517479
16 285308661456109
17 302641427774831
18 317573913751019
19 321027175754629
20 336866824130521
21 357331796744339
22 1020878431297169
23 1082897744693371
24 1148684789012489
25 9295070881578575111
26 9859755075476219149
27 10458744358910058191
28 29880090805636839461
29 31695334089430275799
30 33259198413230468851
31 33620855089606540541
32 35279725624365333809
33 37423001741237879131
34 106915577231321212201
35 113410797903992051459
36 973463478356842592799919
37 1032602289299548955255621
38 1095333837964291484285239
39 3129312029983540559911069
40 3319420643851943354153471
41 3483202590619213772296379
42 3694810384914157044482761
43 11197161487859039232598529
44 101949856624833767901342716951
45 108143405156052462534965931709
46 327729719588146219298926345301
47 364792324112959639158827476291
48 10677106534462215678539721403561279
doneA Simpler Approach
This is a somewhat simpler approach for finding the factors of smaller numbers (less than one million).
print "ROSETTA CODE - Factors of an integer"
'A simpler approach for smaller numbers
[Start]
print
input "Enter an integer (< 1,000,000): "; n
n=abs(int(n)): if n=0 then goto [Quit]
if n>999999 then goto [Start]
FactorCount=FactorCount(n)
select case FactorCount
case 1: print "The factor of 1 is: 1"
case else
print "The "; FactorCount; " factors of "; n; " are: ";
for x=1 to FactorCount
print " "; Factor(x);
next x
if FactorCount=2 then print " (Prime)" else print
end select
goto [Start]
[Quit]
print "Program complete."
end
function FactorCount(n)
dim Factor(100)
for y=1 to n
if y>sqr(n) and FactorCount=1 then
'If no second factor is found by the square root of n, then n is prime.
FactorCount=2: Factor(FactorCount)=n: exit function
end if
if (n mod y)=0 then
FactorCount=FactorCount+1
Factor(FactorCount)=y
end if
next y
end function- Output:
ROSETTA CODE - Factors of an integer Enter an integer (< 1,000,000): 1 The factor of 1 is: 1 Enter an integer (< 1,000,000): 2 The 2 factors of 2 are: 1 2 (Prime) Enter an integer (< 1,000,000): 4 The 3 factors of 4 are: 1 2 4 Enter an integer (< 1,000,000): 6 The 4 factors of 6 are: 1 2 3 6 Enter an integer (< 1,000,000): 999999 The 64 factors of 999999 are: 1 3 7 9 11 13 21 27 33 37 39 63 77 91 99 111 117 143 189 231 259 273 297 333 351 407 429 481 693 777 819 999 1001 1221 1287 1443 2079 2331 2457 2849 3003 3367 3663 3861 4329 5291 6993 8547 9009 10101 10989 12987 15873 25641 27027 30303 37037 47619 76923 90909 111111 142857 333333 999999 Enter an integer (< 1,000,000): Program complete.
Minimal BASIC
10 REM Factors of an integer
20 PRINT "Enter an integer";
30 INPUT N
40 IF N = 0 THEN 30
50 N1 = ABS(N)
60 FOR I = 1 TO N1/2
70 IF INT(N1/I)*I <> N1 THEN 90
80 PRINT I;
90 NEXT I
100 PRINT N1
110 END
MSX Basic
10 INPUT "Enter an integer: "; N
20 IF N = 0 THEN GOTO 10
30 N1 = ABS(N)
40 FOR I = 1 TO N1/2
50 IF N1 MOD I = 0 THEN PRINT I;
60 NEXT I
70 PRINT N1
Nascom BASIC
10 REM Factors of an integer
20 INPUT "Enter an integer"; N
30 IF N=0 THEN 20
40 NA=ABS(N)
50 FOR I=1 TO INT(NA/2)
60 IF NA=INT(NA/I)*I THEN PRINT I;
70 NEXT I
80 PRINT NA
90 END
- Output:
Enter an integer? 60 1 2 3 4 5 6 10 12 15 20 30 60
See also Minimal BASIC
Palo Alto Tiny BASIC
10 REM FACTORS OF AN INTEGER
20 INPUT "ENTER AN INTEGER"N
30 IF N=0 GOTO 20
40 LET A=ABS(N)
50 IF A=1 GOTO 90
60 FOR I=1 TO A/2
70 IF (A/I)*I=A PRINT I," ",
80 NEXT I
90 PRINT A
100 STOP
- Output:
3 runs.
ENTER AN INTEGER:1
1
ENTER AN INTEGER:60
1 2 3 4 5 6 10 12 15 20 30 60
ENTER AN INTEGER:-22222
1 2 41 82 271 542 11111 22222
PureBasic
Procedure PrintFactors(n)
Protected i, lim=Round(sqr(n),#PB_Round_Up)
NewList F.i()
For i=1 To lim
If n%i=0
AddElement(F()): F()=i
AddElement(F()): F()=n/i
EndIf
Next
;- Present the result
SortList(F(),#PB_Sort_Ascending)
ForEach F()
Print(str(F())+" ")
Next
EndProcedure
If OpenConsole()
Print("Enter integer to factorize: ")
PrintFactors(Val(Input()))
Print(#CRLF$+#CRLF$+"Press ENTER to quit."): Input()
EndIf
- Output:
Enter integer to factorize: 96 1 2 3 4 6 8 12 16 24 32 48 96
QB64
'Task
'Compute the factors of a positive integer.
'These factors are the positive integers by which the number being factored can be divided to yield a positive integer result.
Dim Dividendum As Integer, Index As Integer
Randomize Timer
Dividendum = Int(Rnd * 1000) + 1
Print " Dividendum: "; Dividendum
Index = Int(Dividendum / 2)
print "Divisors: ";
While Index > 0
If Dividendum Mod Index = 0 Then Print Index; " ";
Index = Index - 1
Wend
EndQBasic
See QuickBASIC.
QuickBASIC
This example stores the factors in a shared array (with the original number as the last element) for later retrieval.
Note that this will error out if you pass 32767 (or higher).
DECLARE SUB factor (what AS INTEGER)
REDIM SHARED factors(0) AS INTEGER
DIM i AS INTEGER, L AS INTEGER
INPUT "Gimme a number"; i
factor i
PRINT factors(0);
FOR L = 1 TO UBOUND(factors)
PRINT ","; factors(L);
NEXT
PRINT
SUB factor (what AS INTEGER)
DIM tmpint1 AS INTEGER
DIM L0 AS INTEGER, L1 AS INTEGER
REDIM tmp(0) AS INTEGER
REDIM factors(0) AS INTEGER
factors(0) = 1
FOR L0 = 2 TO what
IF (0 = (what MOD L0)) THEN
'all this REDIMing and copying can be replaced with:
'REDIM PRESERVE factors(UBOUND(factors)+1)
'in languages that support the PRESERVE keyword
REDIM tmp(UBOUND(factors)) AS INTEGER
FOR L1 = 0 TO UBOUND(factors)
tmp(L1) = factors(L1)
NEXT
REDIM factors(UBOUND(factors) + 1) AS INTEGER
FOR L1 = 0 TO UBOUND(factors) - 1
factors(L1) = tmp(L1)
NEXT
factors(UBOUND(factors)) = L0
END IF
NEXT
END SUB
- Output:
Gimme a number? 17 1 , 17 Gimme a number? 12345 1 , 3 , 5 , 15 , 823 , 2469 , 4115 , 12345 Gimme a number? 32765 1 , 5 , 6553 , 32765 Gimme a number? 32766 1 , 2 , 3 , 6 , 43 , 86 , 127 , 129 , 254 , 258 , 381 , 762 , 5461 , 10922 , 16383 , 32766
Quite BASIC
10 INPUT "Enter an integer: "; N
20 IF N = 0 THEN GOTO 15
30 N1 = ABS(N)
40 FOR I = 1 TO N1/2
50 IF N1 - INT(N1 / I) * I = 0 THEN PRINT I; " ";
60 NEXT I
70 PRINT N1
REALbasic
Function factors(num As UInt64) As UInt64()
'This function accepts an unsigned 64 bit integer as input and returns an array of unsigned 64 bit integers
Dim result() As UInt64
Dim iFactor As UInt64 = 1
While iFactor <= num/2 'Since a factor will never be larger than half of the number
If num Mod iFactor = 0 Then
result.Append(iFactor)
End If
iFactor = iFactor + 1
Wend
result.Append(num) 'Since a given number is always a factor of itself
Return result
End Function
Run BASIC
PRINT "Factors of 45 are ";factorlist$(45)
PRINT "Factors of 12345 are "; factorlist$(12345)
END
FUNCTION factorlist$(f)
DIM L(100)
FOR i = 1 TO SQR(f)
IF (f MOD i) = 0 THEN
L(c) = i
c = c + 1
IF (f <> i^2) THEN
L(c) = (f / i)
c = c + 1
END IF
END IF
NEXT i
s = 1
WHILE s = 1
s = 0
FOR i = 0 TO c-1
IF L(i) > L(i+1) AND L(i+1) <> 0 THEN
t = L(i)
L(i) = L(i+1)
L(i+1) = t
s = 1
END IF
NEXT i
WEND
FOR i = 0 TO c-1
factorlist$ = factorlist$ + STR$(L(i)) + ", "
NEXT
END FUNCTION
- Output:
Factors of 45 are 1, 3, 5, 9, 15, 45, Factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345,
Sinclair ZX81 BASIC
10 INPUT N
20 FOR I=1 TO N
30 IF N/I=INT (N/I) THEN PRINT I;" ";
40 NEXT I
- Input:
315
- Output:
1 3 5 7 9 15 35 45 63 105 315
Tiny BASIC
100 PRINT "Give me a number:"
110 INPUT I
120 LET C=1
130 PRINT "Factors of ",I,":"
140 IF I/C*C=I THEN PRINT C
150 LET C=C+1
160 IF C<=I THEN GOTO 140
170 END
- Output:
Give me a number: 60 Factors of 60: 1 2 3 4 5 6 10 12 15 20 30 60
True BASIC
SUB printfactors(n)
IF n < 1 THEN EXIT SUB
PRINT n; "=>";
FOR i = 1 TO n / 2
IF REMAINDER(n, i) = 0 THEN PRINT i;
NEXT i
PRINT n
END SUB
CALL printfactors(11)
CALL printfactors(21)
CALL printfactors(32)
CALL printfactors(45)
CALL printfactors(67)
CALL printfactors(96)
END
VBA
Function Factors(x As Integer) As String
Application.Volatile
Dim i As Integer
Dim cooresponding_factors As String
Factors = 1
corresponding_factors = x
For i = 2 To Sqr(x)
If x Mod i = 0 Then
Factors = Factors & ", " & i
If i <> x / i Then corresponding_factors = x / i & ", " & corresponding_factors
End If
Next i
If x <> 1 Then Factors = Factors & ", " & corresponding_factors
End Function
- Output:
cell formula is "=Factors(840)" resultant value is "1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840"
XBasic
PROGRAM "Factors of an integer"
VERSION "0.0000"
DECLARE FUNCTION Entry ()
DECLARE FUNCTION printFactors (n)
FUNCTION Entry ()
printFactors(11)
printFactors(21)
printFactors(32)
printFactors(45)
printFactors(67)
printFactors(96)
END FUNCTION
FUNCTION printFactors (n)
PRINT n; " =>";
FOR i = 1 TO n / 2
IF n MOD i = 0 THEN PRINT i; " ";
NEXT i
PRINT n
END FUNCTION
END PROGRAM
Yabasic
sub printFactors(n)
if n < 1 return 0
print n, " =>";
for i = 1 to n / 2
if mod(n, i) = 0 print i, " ";
next i
print n
end sub
printFactors(11)
printFactors(21)
printFactors(32)
printFactors(45)
printFactors(67)
printFactors(96)
print
endZX Spectrum Basic
10 INPUT "Enter a number or 0 to exit: ";n
20 IF n=0 THEN STOP
30 PRINT "Factors of ";n;": ";
40 FOR i=1 TO n
50 IF FN m(n,i)=0 THEN PRINT i;" ";
60 NEXT i
70 DEF FN m(a,b)=a-INT (a/b)*b
Batch File
Command line version:
@echo off
set res=Factors of %1:
for /L %%i in (1,1,%1) do call :fac %1 %%i
echo %res%
goto :eof
:fac
set /a test = %1 %% %2
if %test% equ 0 set res=%res% %2
- Output:
>factors 32767 Factors of 32767: 1 7 31 151 217 1057 4681 32767 >factors 45 Factors of 45: 1 3 5 9 15 45 >factors 53 Factors of 53: 1 53 >factors 64 Factors of 64: 1 2 4 8 16 32 64 >factors 100 Factors of 100: 1 2 4 5 10 20 25 50 100
Interactive version:
@echo off
set /p limit=Gimme a number:
set res=Factors of %limit%:
for /L %%i in (1,1,%limit%) do call :fac %limit% %%i
echo %res%
goto :eof
:fac
set /a test = %1 %% %2
if %test% equ 0 set res=%res% %2
- Output:
>factors Gimme a number:27 Factors of 27: 1 3 9 27 >factors Gimme a number:102 Factors of 102: 1 2 3 6 17 34 51 102
bc
/* Calculate the factors of n and return their count.
* This function mutates the global array f[] which will
* contain all factors of n in ascending order after the call!
*/
define f(n) {
auto i, d, h, h[], l, o
/* Local variables:
* i: Loop variable.
* d: Complementary (higher) factor to i.
* h: Will always point to the last element of h[].
* h[]: Array to hold the greater factor of the pair (x, y), where
* x * y == n. The factors are stored in descending order.
* l: Will always point to the next free spot in f[].
* o: For saving the value of scale.
*/
/* Use integer arithmetic */
o = scale
scale = 0
/* Two factors are 1 and n (if n != 1) */
f[l++] = 1
if (n == 1) return(1)
h[0] = n
/* Main loop */
for (i = 2; i < h[h]; i++) {
if (n % i == 0) {
d = n / i
if (d != i) {
h[++h] = d
}
f[l++] = i
}
}
/* Append the values in h[] to f[] */
while (h >= 0) {
f[l++] = h[h--]
}
scale = o
return(l)
}
Befunge
10:p&v: >:0:g%#v_0:g\:0:g/\v
>:0:g:*`| > >0:g1+0:p
>:0:g:*-#v_0:g\>$>:!#@_.v
> ^ ^ ," "<
BQN
A bqncrate idiom.
Factors ← (1+↕)⊸(⊣/˜0=|)
•Show Factors 12345
•Show Factors 729
⟨ 1 3 5 15 823 2469 4115 12345 ⟩
⟨ 1 3 9 27 81 243 729 ⟩
The primes library from bqn-libs can be used for a solution that's more efficient for large inputs. FactorExponents returns each unique prime factor along with its exponent.
⟨FactorExponents⟩ ← •Import "primes.bqn" # With appropriate path
Factors ← { ∧⥊ 1 ×⌜´ ⋆⟜(↕1+⊢)¨˝ FactorExponents 𝕩 }
Burlesque
blsq ) 32767 fc
{1 7 31 151 217 1057 4681 32767}C
#include <stdio.h>
#include <stdlib.h>
typedef struct {
int *list;
short count;
} Factors;
void xferFactors( Factors *fctrs, int *flist, int flix )
{
int ix, ij;
int newSize = fctrs->count + flix;
if (newSize > flix) {
fctrs->list = realloc( fctrs->list, newSize * sizeof(int));
}
else {
fctrs->list = malloc( newSize * sizeof(int));
}
for (ij=0,ix=fctrs->count; ix<newSize; ij++,ix++) {
fctrs->list[ix] = flist[ij];
}
fctrs->count = newSize;
}
Factors *factor( int num, Factors *fctrs)
{
int flist[301], flix;
int dvsr;
flix = 0;
fctrs->count = 0;
free(fctrs->list);
fctrs->list = NULL;
for (dvsr=1; dvsr*dvsr < num; dvsr++) {
if (num % dvsr != 0) continue;
if ( flix == 300) {
xferFactors( fctrs, flist, flix );
flix = 0;
}
flist[flix++] = dvsr;
flist[flix++] = num/dvsr;
}
if (dvsr*dvsr == num)
flist[flix++] = dvsr;
if (flix > 0)
xferFactors( fctrs, flist, flix );
return fctrs;
}
int main(int argc, char*argv[])
{
int nums2factor[] = { 2059, 223092870, 3135, 45 };
Factors ftors = { NULL, 0};
char sep;
int i,j;
for (i=0; i<4; i++) {
factor( nums2factor[i], &ftors );
printf("\nfactors of %d are:\n ", nums2factor[i]);
sep = ' ';
for (j=0; j<ftors.count; j++) {
printf("%c %d", sep, ftors.list[j]);
sep = ',';
}
printf("\n");
}
return 0;
}
Prime factoring
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* 65536 = 2^16, so we can factor all 32 bit ints */
char bits[65536];
typedef unsigned long ulong;
ulong primes[7000], n_primes;
typedef struct { ulong p, e; } prime_factor; /* prime, exponent */
void sieve()
{
int i, j;
memset(bits, 1, 65536);
bits[0] = bits[1] = 0;
for (i = 0; i < 256; i++)
if (bits[i])
for (j = i * i; j < 65536; j += i)
bits[j] = 0;
/* collect primes into a list. slightly faster this way if dealing with large numbers */
for (i = j = 0; i < 65536; i++)
if (bits[i]) primes[j++] = i;
n_primes = j;
}
int get_prime_factors(ulong n, prime_factor *lst)
{
ulong i, e, p;
int len = 0;
for (i = 0; i < n_primes; i++) {
p = primes[i];
if (p * p > n) break;
for (e = 0; !(n % p); n /= p, e++);
if (e) {
lst[len].p = p;
lst[len++].e = e;
}
}
return n == 1 ? len : (lst[len].p = n, lst[len].e = 1, ++len);
}
int ulong_cmp(const void *a, const void *b)
{
return *(const ulong*)a < *(const ulong*)b ? -1 : *(const ulong*)a > *(const ulong*)b;
}
int get_factors(ulong n, ulong *lst)
{
int n_f, len, len2, i, j, k, p;
prime_factor f[100];
n_f = get_prime_factors(n, f);
len2 = len = lst[0] = 1;
/* L = (1); L = (L, L * p**(1 .. e)) forall((p, e)) */
for (i = 0; i < n_f; i++, len2 = len)
for (j = 0, p = f[i].p; j < f[i].e; j++, p *= f[i].p)
for (k = 0; k < len2; k++)
lst[len++] = lst[k] * p;
qsort(lst, len, sizeof(ulong), ulong_cmp);
return len;
}
int main()
{
ulong fac[10000];
int len, i, j;
ulong nums[] = {3, 120, 1024, 2UL*2*2*2*3*3*3*5*5*7*11*13*17*19 };
sieve();
for (i = 0; i < 4; i++) {
len = get_factors(nums[i], fac);
printf("%lu:", nums[i]);
for (j = 0; j < len; j++)
printf(" %lu", fac[j]);
printf("\n");
}
return 0;
}
- Output:
3: 1 3 120: 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 1024: 1 2 4 8 16 32 64 128 256 512 1024 3491888400: 1 2 3 4 5 6 7 8 9 10 11 ...(>1900 numbers)... 1163962800 1745944200 3491888400
C#
C# 1.0
static void Main (string[] args) {
do {
Console.WriteLine ("Number:");
Int64 p = 0;
do {
try {
p = Convert.ToInt64 (Console.ReadLine ());
break;
} catch (Exception) { }
} while (true);
Console.WriteLine ("For 1 through " + ((int) Math.Sqrt (p)).ToString () + "");
for (int x = 1; x <= (int) Math.Sqrt (p); x++) {
if (p % x == 0)
Console.WriteLine ("Found: " + x.ToString () + ". " + p.ToString () + " / " + x.ToString () + " = " + (p / x).ToString ());
}
Console.WriteLine ("Done.");
} while (true);
}
- Output:
Number: 32434243 For 1 through 5695 Found: 1. 32434243 / 1 = 32434243 Found: 307. 32434243 / 307 = 105649 Done.
C# 3.0
using System;
using System.Collections.Generic;
using System.Linq;
public static class Extension {
public static List<int> Factors (this int me) {
return Enumerable.Range (1, me).Where (x => me % x == 0).ToList ();
}
}
class Program {
static void Main (string[] args) {
Console.WriteLine (String.Join (", ", 45. Factors ()));
}
}
- Output:
1, 3, 5, 9, 15, 45
C++
#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <iterator>
std::vector<int> GenerateFactors(int n) {
std::vector<int> factors = { 1, n };
for (int i = 2; i * i <= n; ++i) {
if (n % i == 0) {
factors.push_back(i);
if (i * i != n)
factors.push_back(n / i);
}
}
std::sort(factors.begin(), factors.end());
return factors;
}
int main() {
const int SampleNumbers[] = { 3135, 45, 60, 81 };
for (size_t i = 0; i < sizeof(SampleNumbers) / sizeof(int); ++i) {
std::vector<int> factors = GenerateFactors(SampleNumbers[i]);
std::cout << "Factors of ";
std::cout.width(4);
std::cout << SampleNumbers[i] << " are: ";
std::copy(factors.begin(), factors.end(), std::ostream_iterator<int>(std::cout, " "));
std::cout << std::endl;
}
return EXIT_SUCCESS;
}
- Output:
Factors of 3135 are: 1 3 5 11 15 19 33 55 57 95 165 209 285 627 1045 3135 Factors of 45 are: 1 3 5 9 15 45 Factors of 60 are: 1 2 3 4 5 6 10 12 15 20 30 60 Factors of 81 are: 1 3 9 27 81
Ceylon
shared void run() {
{Integer*} getFactors(Integer n) =>
(1..n).filter((Integer element) => element.divides(n));
for(Integer i in 1..100) {
print("the factors of ``i`` are ``getFactors(i)``");
}
}
Chapel
Inspired by the Clojure solution:
iter factors(n) {
for i in 1..floor(sqrt(n)):int {
if n % i == 0 then {
yield i;
yield n / i;
}
}
}
Clojure
(defn factors [n]
(filter #(zero? (rem n %)) (range 1 (inc n))))
(print (factors 45))
(1 3 5 9 15 45)
Improved version. Considers small factors from 1 up to (sqrt n) -- we increment it because range does not include the end point. Pair each small factor with its co-factor, flattening the results, and put them into a sorted set to get the factors in order.
(defn factors [n]
(into (sorted-set)
(mapcat (fn [x] [x (/ n x)])
(filter #(zero? (rem n %)) (range 1 (inc (Math/sqrt n)))) )))
Same idea, using for comprehensions.
(defn factors [n]
(into (sorted-set)
(reduce concat
(for [x (range 1 (inc (Math/sqrt n))) :when (zero? (rem n x))]
[x (/ n x)]))))
CLU
isqrt = proc (s: int) returns (int)
x0: int := s/2
if x0=0 then return(s) end
x1: int := (x0 + s/x0)/2
while x1<x0 do
x0, x1 := x1, (x1 + s/x1)/2
end
return(x0)
end isqrt
factors = iter (n: int) yields (int)
yield(1)
for i: int in int$from_to(2,isqrt(n)) do
if n//i=0 then
yield(i)
if i*i ~= n then yield(n/i) end
end
end
yield(n)
end factors
start_up = proc ()
po: stream := stream$primary_output()
a: array[int] := array[int]$[3135, 45, 64, 53, 45, 81]
for n: int in array[int]$elements(a) do
stream$puts(po, "Factors of " || int$unparse(n) || ":")
for f: int in factors(n) do
stream$puts(po, " " || int$unparse(f))
end
stream$putl(po, "")
end
end start_up- Output:
Factors of 3135: 1 3 1045 5 627 11 285 15 209 19 165 33 95 55 57 3135 Factors of 45: 1 3 15 5 9 45 Factors of 64: 1 2 32 4 16 8 64 Factors of 53: 1 53 Factors of 45: 1 3 15 5 9 45 Factors of 81: 1 3 27 9 81
COBOL
IDENTIFICATION DIVISION.
PROGRAM-ID. FACTORS.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 CALCULATING.
03 NUM USAGE BINARY-LONG VALUE ZERO.
03 LIM USAGE BINARY-LONG VALUE ZERO.
03 CNT USAGE BINARY-LONG VALUE ZERO.
03 DIV USAGE BINARY-LONG VALUE ZERO.
03 REM USAGE BINARY-LONG VALUE ZERO.
03 ZRS USAGE BINARY-SHORT VALUE ZERO.
01 DISPLAYING.
03 DIS PIC 9(10) USAGE DISPLAY.
PROCEDURE DIVISION.
MAIN-PROCEDURE.
DISPLAY "Factors of? " WITH NO ADVANCING
ACCEPT NUM
DIVIDE NUM BY 2 GIVING LIM.
PERFORM VARYING CNT FROM 1 BY 1 UNTIL CNT > LIM
DIVIDE NUM BY CNT GIVING DIV REMAINDER REM
IF REM = 0
MOVE CNT TO DIS
PERFORM SHODIS
END-IF
END-PERFORM.
MOVE NUM TO DIS.
PERFORM SHODIS.
STOP RUN.
SHODIS.
MOVE ZERO TO ZRS.
INSPECT DIS TALLYING ZRS FOR LEADING ZERO.
DISPLAY DIS(ZRS + 1:)
EXIT PARAGRAPH.
END PROGRAM FACTORS.
CoffeeScript
# Reference implementation for finding factors is slow, but hopefully
# robust--we'll use it to verify the more complicated (but hopefully faster)
# algorithm.
slow_factors = (n) ->
(i for i in [1..n] when n % i == 0)
# The rest of this code does two optimizations:
# 1) When you find a prime factor, divide it out of n (smallest_prime_factor).
# 2) Find the prime factorization first, then compute composite factors from those.
smallest_prime_factor = (n) ->
for i in [2..n]
return n if i*i > n
return i if n % i == 0
prime_factors = (n) ->
return {} if n == 1
spf = smallest_prime_factor n
result = prime_factors(n / spf)
result[spf] or= 0
result[spf] += 1
result
fast_factors = (n) ->
prime_hash = prime_factors n
exponents = []
for p of prime_hash
exponents.push
p: p
exp: 0
result = []
while true
factor = 1
for obj in exponents
factor *= Math.pow obj.p, obj.exp
result.push factor
break if factor == n
# roll the odometer
for obj, i in exponents
if obj.exp < prime_hash[obj.p]
obj.exp += 1
break
else
obj.exp = 0
return result.sort (a, b) -> a - b
verify_factors = (factors, n) ->
expected_result = slow_factors n
throw Error("wrong length") if factors.length != expected_result.length
for factor, i in expected_result
console.log Error("wrong value") if factors[i] != factor
for n in [1, 3, 4, 8, 24, 37, 1001, 11111111111, 99999999999]
factors = fast_factors n
console.log n, factors
if n < 1000000
verify_factors factors, n
- Output:
> coffee factors.coffee 1 [ 1 ] 3 [ 1, 3 ] 4 [ 1, 2, 4 ] 8 [ 1, 2, 4, 8 ] 24 [ 1, 2, 3, 4, 6, 8, 12, 24 ] 37 [ 1, 37 ] 1001 [ 1, 7, 11, 13, 77, 91, 143, 1001 ] 11111111111 [ 1, 21649, 513239, 11111111111 ] 99999999999 [ 1, 3, 9, 21649, 64947, 194841, 513239, 1539717, 4619151, 11111111111, 33333333333, 99999999999 ]
Common Lisp
We iterate in the range 1..sqrt(n) collecting ‘low’ factors and corresponding ‘high’ factors, and combine at the end to produce an ordered list of factors.
(defun factors (n &aux (lows '()) (highs '()))
(do ((limit (1+ (isqrt n))) (factor 1 (1+ factor)))
((= factor limit)
(when (= n (* limit limit))
(push limit highs))
(remove-duplicates (nreconc lows highs)))
(multiple-value-bind (quotient remainder) (floor n factor)
(when (zerop remainder)
(push factor lows)
(push quotient highs)))))
Crystal
Brute force and slow, by checking every value up to n.
struct Int
def factors() (1..self).select { |n| (self % n).zero? } end
end
Faster, by only checking values up to .
struct Int
def factors
f = [] of Int32
(1..Math.sqrt(self)).each{ |i|
(f << i; f << self // i if self // i != i) if (self % i).zero?
}
f.sort
end
end
Tests:
[45, 53, 64].each {|n| puts "#{n} : #{n.factors}"}
- Output:
45 : [1, 3, 5, 9, 15, 45] 53 : [1, 53] 64 : [1, 2, 4, 8, 16, 32, 64]
D
Procedural Style
import std.stdio, std.math, std.algorithm;
T[] factors(T)(in T n) pure nothrow {
if (n == 1)
return [n];
T[] res = [1, n];
T limit = cast(T)real(n).sqrt + 1;
for (T i = 2; i < limit; i++) {
if (n % i == 0) {
res ~= i;
immutable q = n / i;
if (q > i)
res ~= q;
}
}
return res.sort().release;
}
void main() {
writefln("%(%s\n%)", [45, 53, 64, 1111111].map!factors);
}
- Output:
[1, 3, 5, 9, 15, 45] [1, 53] [1, 2, 4, 8, 16, 32, 64] [1, 239, 4649, 1111111]
Functional Style
import std.stdio, std.algorithm, std.range;
auto factors(I)(I n) {
return iota(1, n + 1).filter!(i => n % i == 0);
}
void main() {
36.factors.writeln;
}
- Output:
[1, 2, 3, 4, 6, 9, 12, 18, 36]
Dart
import 'dart:math';
factors(n)
{
var factorsArr = [];
factorsArr.add(n);
factorsArr.add(1);
for(var test = n - 1; test >= sqrt(n).toInt(); test--)
if(n % test == 0)
{
factorsArr.add(test);
factorsArr.add(n / test);
}
return factorsArr;
}
void main() {
print(factors(5688));
}
Dc
Simple O(n) version
[Enter positive number: ]P ? sn
[Factors of ]P lnn [ are: ]P
[q]sq 1si [[ ]P lin]sp [ li ln <q ln li % 0=p li1+si lxx ]dsxx AP- Output:
Factors of 998877 are: 1 3 11 33 30269 90807 332959 998877 0m1.120s
Faster O(sqrt(n)) version
[Enter positive number: ]P ? sn
[Factors of ]P lnn [ are: ]P
[q]sq lnvsv 1si 0sj [[ ]P lin]sp [lkSb lj1+sj]sa [lpx ln li /dsk li<a ]sP
[li lv <q ln li % 0=P li1+si lxx]dsxx
[lj 1>q lj1-sj Lbsi lpx lxx]dsxx AP0m0.004s
Delphi
See #Pascal.
DuckDB
DuckDB allows both functional and table-oriented approaches to solving problems such as finding the factors of a number, and solutions using both approaches are presented here.
Functional Approach
The following function produces a list of the sorted factors.
create or replace function factors(n) as
list_filter( generate_series(1, sqrt(n)::INT), i -> n % i = 0)
.list_transform(i -> if (n // i = i, [i], [i, n//i]))
.flatten()
.list_sort() ;
## Examples
select n, factors(n) from (select unnest([1,2,3,4,5,6, 45, 53, 64]) as n);
- Output:
┌───────┬──────────────────────────┐ │ n │ factors(n) │ │ int32 │ int64[] │ ├───────┼──────────────────────────┤ │ 1 │ [1] │ │ 2 │ [1, 2] │ │ 3 │ [1, 3] │ │ 4 │ [1, 2, 4] │ │ 5 │ [1, 5] │ │ 6 │ [1, 2, 3, 6] │ │ 45 │ [1, 3, 5, 9, 15, 45] │ │ 53 │ [1, 53] │ │ 64 │ [1, 2, 4, 8, 16, 32, 64] │ └───────┴──────────────────────────┘
Tabular Approach
The following function produces a table of the factors without sorting them.
create or replace function unsorted_factors(n) as table (
with cte as (
select i
from generate_series(1, sqrt(n)::INT) _(i)
where n % i = 0
)
from cte
union all
(select n//i
from cte
where n // i != i)
);
## Examples
from unsorted_factors(99);
select n, (select array_agg(x) from unsorted_factors(n) _(x)) as unsorted_factors
from (select unnest([1,2,3,4,5,6, 45, 53, 64]) as n);
- Output:
┌───────┐ │ i │ │ int64 │ ├───────┤ │ 1 │ │ 3 │ │ 9 │ │ 99 │ │ 33 │ │ 11 │ └───────┘ ┌───────┬──────────────────────────┐ │ n │ factors │ │ int32 │ int64[] │ ├───────┼──────────────────────────┤ │ 1 │ [1] │ │ 2 │ [2, 1] │ │ 3 │ [3, 1] │ │ 4 │ [4, 1, 2] │ │ 5 │ [1, 5] │ │ 6 │ [6, 3, 1, 2] │ │ 45 │ [45, 15, 9, 1, 3, 5] │ │ 53 │ [53, 1] │ │ 64 │ [1, 2, 4, 8, 64, 32, 16] │ └───────┴──────────────────────────┘
Dyalect
func Iterator.Where(pred) {
for x in this when pred(x) {
yield x
}
}
func Integer.Factors() {
(1..this).Where(x => this % x == 0)
}
for x in 45.Factors() {
print(x)
}Output:
1 3 5 9 15 45
E
def factors(x :(int > 0)) {
var xfactors := []
for f ? (x % f <=> 0) in 1..x {
xfactors with= f
}
return xfactors
}EasyLang
n = 720
for i = 1 to n
if n mod i = 0
factors[] &= i
.
.
print factors[]
EchoLisp
prime-factors gives the list of n's prime-factors. We mix them to get all the factors.
;; ppows
;; input : a list g of grouped prime factors ( 3 3 3 ..)
;; returns (1 3 9 27 ...)
(define (ppows g (mult 1))
(for/fold (ppows '(1)) ((a g))
(set! mult (* mult a))
(cons mult ppows)))
;; factors
;; decomp n into ((2 2 ..) ( 3 3 ..) ) prime factors groups
;; combines (1 2 4 8 ..) (1 3 9 ..) lists
(define (factors n)
(list-sort <
(if (<= n 1) '(1)
(for/fold (divs'(1)) ((g (map ppows (group (prime-factors n)))))
(for*/list ((a divs) (b g)) (* a b))))))
- Output:
(lib 'bigint)
(factors 666)
→ (1 2 3 6 9 18 37 74 111 222 333 666)
(length (factors 108233175859200))
→ 666 ;; 💀
(define huge 1200034005600070000008900000000000000000)
(time ( length (factors huge)))
→ (394ms 7776)
EDSAC order code
Input is limited to 10 decimal digits, which is as many as the EDSAC print subroutine P7 can handle. Factors are printed in pairs, such that the product of the factors in each pair equals the input number.
2021-10-10 Integers are now read from the tape in decimal format, instead of being defined by the awkward method of pseudo-orders. The factorization of 999,999,999 has been removed, as it took too long on the commonly-used EdsacPC simulator (14.6 million orders - over 6 hours on the original EDSAC).
[Factors of an integer, from Rosetta Code website.]
[EDSAC program, Initial Orders 2.]
[The numbers to be factorized are read in by library subroutine R2
(Wilkes, Wheeler and Gill, 1951 edition, pp.96-97, 148).]
[The address of the integers is placed in location 46, so they can be
referred to by the N parameter (or we could have used 45 and H, etc.)]
T 46 K
P 600 F [address of integers]
[Subroutine R2]
GKT20FVDL8FA40DUDTFI40FA40FS39FG@S2FG23FA5@T5@E4@E13Z
T #N [pass address of integers to R2]
[List of integers to be factorized; edit ad lib. R2 requires 'F' after
each integer except the last, and '#' (pi) after the last.
This program uses 0 to mark the end of the list.]
42000F999999F0#
T Z [resume normal loading]
[Modified library subroutine P7.]
[Prints signed integer; up to 10 digits, left-justified.]
[Input: 0D = integer,]
[54 locations. Load at even address. Workspace 4D.]
T 56 K
GKA3FT42@A49@T31@ADE10@T31@A48@T31@SDTDH44#@NDYFLDT4DS43@
TFH17@S17@A43@G23@UFS43@T1FV4DAFG50@SFLDUFXFOFFFSFL4FT4DA49@
T31@A1FA43@G20@XFP1024FP610D@524D!FO46@O26@XFSFL8FT4DE39@
[Division subroutine for positive long integers.
35-bit dividend and divisor (max 2^34 - 1)
returning quotient and remainder.
Input: dividend at 4D, divisor at 6D
Output: remainder at 4D, quotient at 6D.
37 locations; working locations 0D, 8D.]
T 110 K
GKA3FT35@A6DU8DTDA4DRDSDG13@T36@ADLDE4@T36@T6DA4DSDG23@
T4DA6DYFYFT6DT36@A8DSDE35@T36@ADRDTDA6DLDT6DE15@EFPF
[********************** ROSETTA CODE TASK **********************]
[Subroutine to find and print factors of a positive integer.
Input: 0D = integer, maximum 10 decimal digits.
Load at even address.]
T 148 K
G K
A 3 F [form and plant link for return]
T 55 @
A D [load integer whose factors are to be found]
T 56#@ [store]
A 62#@ [load 1]
T 58#@ [possible factor := 1]
S 65 @ [negative count of items per line]
T 64 @ [initialize count]
[Start of loop round possible factors]
[8] T F [clear acc]
A 56#@ [load integer]
T 4 D [to 4F for division]
A 58#@ [load possible factor]
T 6 D [to 6F for division]
A 13 @ [for return from next]
G 110 F [do division; clears acc]
A 6 D [save quotient (6F may be changed below)]
T 60#@
S 4 D [load negative of remainder]
G 44 @ [skip if remainder > 0]
[Here if m is a factor of n.]
[Print m and the quotient together]
T F [clear acc]
A 64 @ [test count of items per line]
G 26 @ [skip if not start of line]
S 65 @ [start of line, reset count]
T 64 @
O 70 @ [and print CR, LF]
O 71 @
[26] T F [clear acc]
O 67 @ [print '(']
A 58#@ [load factor]
T D [to 0D for printing]
A 30 @ [for return from next]
G 56 F [print factor; clears acc]
O 69 @ [print comma]
A 60#@ [load quotient]
T D [to 0D for printing]
A 35 @ [for return from next]
G 56 F [print quotient; clears acc]
O 68 @ [print ')']
A 64 @ [negative counter for items per line]
A 2 F [inc]
E 43 @ [skip if end of line]
O 66 @ [not end of line, print 2 spaces]
O 66 @
[43] T 64 @ [update counter]
[Common code after testing possible factor]
[44] T F [clear acc]
A 58#@ [load possible factor]
A 62#@ [inc by 1]
U 58#@ [store back]
S 60#@ [compare with quotient]
G 8 @ [loop if (new factor) < (old quotient)]
[Here when found all factors]
O 70 @ [print CR, LF twice]
O 71 @
O 70 @
O 71 @
T F [exit with acc = 0]
[55] E F [return]
[--------]
[56] PF PF [number whose factors are to be found]
[58] PF PF [possible factor]
[60] PF PF [integer part of (number/factor)]
T62#Z PF [clear sandwich digit in 35-bit constant 1]
T 62 Z [resume normal loading]
[62] PD PF [35-bit constant 1]
[64] P F [negative counter for items per line]
[65] P 4 F [items per line, in address field]
[66] ! F [space]
[67] K F [left parenthesis (in figures mode)]
[68] L F [right parenthesis (in figures mode)]
[69] N F [comma (in figures mode)]
[70] @ F [carriage return]
[71] & F [line feed]
[Main routine for demonstrating subroutine.]
T 400 K
G K
[0] # F [set figures mode]
[1] K 4096 F [null char]
[2] S #N [order to load negative of first number]
[3] P 2 F [to inc address by 2 for next number]
[Enter with acc = 0]
[4] O @ [set teleprinter to figures]
A 2 @ [load order for first integer]
[6] T 7 @ [plant in next order]
[7] S D [load negative of 35-bit integer]
E 17 @ [exit if number is 0]
T D [negative to 0D]
S D [convert to positive]
T D [pass to subroutine]
A 12 @ [call subroutine to find and print factors]
G 148 F
A 7 @ [modify order above, for next integer]
A 3 @
E 6 @ [always jump, since S = 12 > 0]
[--------]
[17] O 1 @ [done, print null to flush printer buffer]
Z F [stop]
E 4 Z [define entry point]
P F [acc = 0 on entry]- Output:
(1,42000) (2,21000) (3,14000) (4,10500) (5,8400) (6,7000) (7,6000) (8,5250) (10,4200) (12,3500) (14,3000) (15,2800) (16,2625) (20,2100) (21,2000) (24,1750) (25,1680) (28,1500) (30,1400) (35,1200) (40,1050) (42,1000) (48,875) (50,840) (56,750) (60,700) (70,600) (75,560) (80,525) (84,500) (100,420) (105,400) (112,375) (120,350) (125,336) (140,300) (150,280) (168,250) (175,240) (200,210) (1,999999) (3,333333) (7,142857) (9,111111) (11,90909) (13,76923) (21,47619) (27,37037) (33,30303) (37,27027) (39,25641) (63,15873) (77,12987) (91,10989) (99,10101) (111,9009) (117,8547) (143,6993) (189,5291) (231,4329) (259,3861) (273,3663) (297,3367) (333,3003) (351,2849) (407,2457) (429,2331) (481,2079) (693,1443) (777,1287) (819,1221) (999,1001)
Ela
Using higher-order function
open list
factors m = filter (\x -> m % x == 0) [1..m]Using comprehension
factors m = [x \\ x <- [1..m] | m % x == 0]Elixir
defmodule RC do
def factor(1), do: [1]
def factor(n) do
(for i <- 1..div(n,2), rem(n,i)==0, do: i) ++ [n]
end
# Recursive (faster version);
def divisor(n), do: divisor(n, 1, []) |> Enum.sort
defp divisor(n, i, factors) when n < i*i , do: factors
defp divisor(n, i, factors) when n == i*i , do: [i | factors]
defp divisor(n, i, factors) when rem(n,i)==0, do: divisor(n, i+1, [i, div(n,i) | factors])
defp divisor(n, i, factors) , do: divisor(n, i+1, factors)
end
Enum.each([45, 53, 60, 64], fn n ->
IO.puts "#{n}: #{inspect RC.factor(n)}"
end)
IO.puts "\nRange: #{inspect range = 1..10000}"
funs = [ factor: &RC.factor/1,
divisor: &RC.divisor/1 ]
Enum.each(funs, fn {name, fun} ->
{time, value} = :timer.tc(fn -> Enum.count(range, &length(fun.(&1))==2) end)
IO.puts "#{name}\t prime count : #{value},\t#{time/1000000} sec"
end)
- Output:
45: [1, 3, 5, 9, 15, 45] 53: [1, 53] 60: [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] 64: [1, 2, 4, 8, 16, 32, 64] Range: 1..10000 factor prime count : 1229, 7.316 sec divisor prime count : 1229, 0.265 sec
EMal
fun factors = List by int n
List result = int[1]
for each int i in range(2, n)
if n % i == 0 do result.append(i) end
end
result.append(n)
return result
end
fun main = int by List args
int n = when(args.length == 0, ask(int, "Enter the number to factor please "), int!args[0])
writeLine(factors(n))
return 0
end
exit main(Runtime.args)- Output:
emal.exe Org\RosettaCode\FactorsOfAnInteger.emal 999997 [1,757,1321,999997]
Erlang
with Built in fuctions
factors(N) ->
[I || I <- lists:seq(1,trunc(N/2)), N rem I == 0]++[N].
Recursive
Another, less concise, but faster version
-module(divs).
-export([divs/1]).
divs(0) -> [];
divs(1) -> [];
divs(N) -> lists:sort(divisors(1,N))++[N].
divisors(1,N) ->
[1] ++ divisors(2,N,math:sqrt(N)).
divisors(K,_N,Q) when K > Q -> [];
divisors(K,N,_Q) when N rem K =/= 0 ->
[] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) when K * K == N ->
[K] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) ->
[K, N div K] ++ divisors(K+1,N,math:sqrt(N)).
- Output:
58> timer:tc(divs, factors, [20000]).
{2237,
[1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,
500,625,800,1000,1250,2000,2500,4000|...]}
59> timer:tc(divs, divs, [20000]).
{106,
[1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,
500,625,800,1000,1250,2000,2500,4000|...]}
The first number is milliseconds. I'v ommitted repeating the first fuction.
ERRE
PROGRAM FACTORS
!$DOUBLE
PROCEDURE FACTORLIST(N->L$)
LOCAL C%,I,FLIPS%,I%
LOCAL DIM L[32]
FOR I=1 TO SQR(N) DO
IF N=I*INT(N/I) THEN
L[C%]=I
C%=C%+1
IF N<>I*I THEN
L[C%]=INT(N/I)
C%=C%+1
END IF
END IF
END FOR
! BUBBLE SORT ARRAY L[]
FLIPS%=1
WHILE FLIPS%>0 DO
FLIPS%=0
FOR I%=0 TO C%-2 DO
IF L[I%]>L[I%+1] THEN SWAP(L[I%],L[I%+1]) FLIPS%=1
END FOR
END WHILE
L$=""
FOR I%=0 TO C%-1 DO
L$=L$+STR$(L[I%])+","
END FOR
L$=LEFT$(L$,LEN(L$)-1)
END PROCEDURE
BEGIN
PRINT(CHR$(12);) ! CLS
FACTORLIST(45->L$)
PRINT("The factors of 45 are ";L$)
FACTORLIST(12345->L$)
PRINT("The factors of 12345 are ";L$)
END PROGRAM- Output:
The factors of 45 are 1, 3, 5, 9, 15, 45 The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345
Excel
LAMBDA
Binding the name FACTORS to a custom function defined by the following LAMBDA expression
in the Name Manager of an Excel workbook.
(See: The LAMBDA worksheet function in Excel)
=LAMBDA(n,
IF(1 < n,
LET(
froot, SQRT(n),
nroot, FLOOR.MATH(froot),
lows, FILTERP(
LAMBDA(x, 0 = MOD(n, x))
)(
ENUMFROMTO(1)(nroot)
),
APPEND(lows)(
LAMBDA(x, n / x)(
REVERSE(
IF(froot <> nroot,
lows,
INIT(lows)
)
)
)
)
),
IF(1 = n, {1}, NA())
)
)
and assuming that in the same worksheet, each of the following names is bound to the reusable generic lambda expression which follows it:
APPEND
=LAMBDA(xs,
LAMBDA(ys,
LET(
nx, ROWS(xs),
rowIndexes, SEQUENCE(nx + ROWS(ys)),
colIndexes, SEQUENCE(
1,
MAX(COLUMNS(xs), COLUMNS(ys))
),
IF(
rowIndexes <= nx,
INDEX(xs, rowIndexes, colIndexes),
INDEX(ys, rowIndexes - nx, colIndexes)
)
)
)
)
ENUMFROMTO
=LAMBDA(a,
LAMBDA(z,
SEQUENCE(1 + z - a, 1, a, 1)
)
)
FILTERP
=LAMBDA(p,
LAMBDA(xs,
FILTER(xs, p(xs))
)
)
INIT
=LAMBDA(xs,
IF(
AND(1=ROWS(xs), ISBLANK(xs)),
NA(),
INDEX(
xs,
SEQUENCE(ROWS(xs)-1, 1, 1, 1)
)
)
)
REVERSE
=LAMBDA(xs,
LET(
n, ROWS(xs),
SORTBY(
xs,
SEQUENCE(n, 1, n, -1)
)
)
)
The FACTORS function, applied to an integer, defines a column of integer values.
Here we define a row instead, by composing FACTORS with the standard TRANSPOSE function.
- Output:
| fx | =TRANSPOSE(FACTORS(A2)) | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | ||
| 1 | N | Factors | ||||||||||||||||
| 2 | 64 | 1 | 2 | 4 | 8 | 16 | 32 | 64 | ||||||||||
| 3 | 120 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | |
| 4 | 123456789 | 1 | 3 | 9 | 3607 | 3803 | 10821 | 11409 | 32463 | 34227 | 13717421 | 41152263 | 123456789 | |||||
| 5 | 2 | 1 | 2 | |||||||||||||||
| 6 | 1 | 1 | ||||||||||||||||
| 7 | 0 | #N/A | ||||||||||||||||
| 8 | -1 | #N/A | ||||||||||||||||
F#
If number % divisor = 0 then both divisor AND number / divisor are factors.
So, we only have to search till sqrt(number).
Also, this is lazily evaluated.
let factors number = seq {
for divisor in 1 .. (float >> sqrt >> int) number do
if number % divisor = 0 then
yield divisor
if number <> 1 then yield number / divisor //special case condition: when number=1 then divisor=(number/divisor), so don't repeat it
}
Prime factoring
[6;120;2048;402642;1206432] |> Seq.iter(fun n->printf "%d :" n; [1..n]|>Seq.filter(fun g->n%g=0)|>Seq.iter(fun n->printf " %d" n); printfn "");;
- Output:
OUTPUT : 6 : 1 2 3 6 120 : 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 2048 : 1 2 4 8 16 32 64 128 256 512 1024 2048 402642 : 1 2 3 6 9 18 22369 44738 67107 134214 201321 402642 120643200 : 1 2 3 4 6 8 9 12 16 18 24 32 36 48 59 71 72 96 118 142 144 177 213 236 284 288 354 426 472 531 568 639 708 852 944 1062 1136 12 78 1416 1704 1888 2124 2272 2556 2832 3408 4189 4248 5112 5664 6816 8378 8496 10224 12567 16756 16992 20448 25134 33512 37701 50268 67024 75402 10053 6 134048 150804 201072 301608 402144 603216 1206432
Factor
USE: math.primes.factors
( scratchpad ) 24 divisors .
{ 1 2 3 4 6 8 12 24 }
FALSE
[1[\$@$@-][\$@$@$@$@\/*=[$." "]?1+]#.%]f:
45f;! 53f;! 64f;!Fish
0v
>i:0(?v'0'%+a*
>~a,:1:>r{% ?vr:nr','ov
^:&:;?(&:+1r:< <
Must be called with pre-polulated value (Positive Integer) in the input stack. Try at Fish Playground[1].
For Input Number :
120
The following output was generated:
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120,
Forth
This is a slightly optimized algorithm, since it realizes there are no factors between n/2 and n. The values are saved on the stack and - in true Forth fashion - printed in descending order.
: factors dup 2/ 1+ 1 do dup i mod 0= if i swap then loop ;
: .factors factors begin dup dup . 1 <> while drop repeat drop cr ;
45 .factors
53 .factors
64 .factors
100 .factors
Alternative version with vectored execution
It's not really idiomatic FORTH to leave a variable number of items on the stack, so instead this version repeatedly calls an execution token for each factor, and it uses a defining word to create a fold over the factors of an integer. This version also only tests up to the square root, which means that items are generated in pairs, rather than in sorted order.
: sq s" dup *" evaluate ; immediate
: factors ( n a xt -- )
swap 2>r 1
BEGIN 2dup sq > WHILE
2dup /mod swap 0= IF
over
r> r@ execute
r@ execute >r
ELSE
drop
THEN 1+
REPEAT
2dup sq = IF
2r> swap execute nip
ELSE
2drop r> rdrop
THEN ;
: <with-factors>
create 2, does> 2@ factors ;
0 :noname nip 1+ ; <with-factors> count-factors
0 ' + <with-factors> sum-factors
0 :noname swap . ; <with-factors> (.factors)
: .factors (.factors) drop ;
- Output:
100 .factors 1 100 2 50 4 25 5 20 10 ok 100 count-factors . 9 ok 100 sum-factors . 217 ok 1 100 + 2 + 50 + 4 + 25 + 5 + 20 + 10 + . 217 ok \ test sum-factors result 77 .factors 1 77 7 11 ok 108 .factors 1 108 2 54 3 36 4 27 6 18 9 12 ok
Fortran
program Factors
implicit none
integer :: i, number
write(*,*) "Enter a number between 1 and 2147483647"
read*, number
do i = 1, int(sqrt(real(number))) - 1
if (mod(number, i) == 0) write (*,*) i, number/i
end do
! Check to see if number is a square
i = int(sqrt(real(number)))
if (i*i == number) then
write (*,*) i
else if (mod(number, i) == 0) then
write (*,*) i, number/i
end if
end program
Frink
Frink has built-in factoring functions which use wheel factoring, trial division, Pollard p-1 factoring, and Pollard rho factoring. It also recognizes some special forms (e.g. Mersenne numbers) and handles them efficiently. Integers can either be decomposed into prime factors or all factors.
The factors[n] function will return the prime decomposition of n.
The allFactors[n, include1=true, includeN=true, sort=true, onlyToSqrt=false] function will return all factors of n. The optional arguments include1 and includeN indicate if the numbers 1 and n are to be included in the results. If the optional argument sort is true, the results will be sorted. If the optional argument onlyToSqrt=true, then only the factors less than or equal to the square root of the number will be produced.
The following produces all factors of n, including 1 and n:
allFactors[n]FunL
Function to compute set of factors:
def factors( n ) = {d | d <- 1..n if d|n}Test:
for x <- [103, 316, 519, 639, 760]
println( 'The set of factors of ' + x + ' is ' + factors(x) )- Output:
The set of factors of 103 is {1, 103}
The set of factors of 316 is {158, 4, 79, 1, 2, 316}
The set of factors of 519 is {1, 3, 173, 519}
The set of factors of 639 is {9, 639, 71, 213, 1, 3}
The set of factors of 760 is {8, 19, 4, 40, 152, 5, 10, 76, 1, 95, 190, 760, 20, 2, 38, 380}
FutureBasic
Function to compute set of factors:
local fn Factors( n as int ) as CFArrayRef
CFMutableArrayRef mutArray = fn MutableArrayNew
for int factor = 1 to sqr(n)
if ( n mod factor == 0 )
MutableArrayAddObject( mutArray, @(factor) )
if ( n/factor != factor )
MutableArrayAddObject( mutArray, @(n/factor) )
end if
end if
next
CFArrayRef result = fn ArraySortedArrayUsingSelector( mutArray, @"compare:" )
end fn = result
mda (0) = {1,2,3,4,5,6,7,8,9,10,20,40,60,80,100,200,300,400,512,677,768,966,1000,1024,2048,4096}
int i, n
for i = 0 to mda_count -1
n = mda_integer(i)
print fn StringWithFormat( @"Factors of %4d: [%@]", n, fn ArrayComponentsJoinedByString( fn Factors( n ), @", " ) )
next
HandleEvents- Output:
Factors of 1: [1] Factors of 2: [1, 2] Factors of 3: [1, 3] Factors of 4: [1, 2, 4] Factors of 5: [1, 5] Factors of 6: [1, 2, 3, 6] Factors of 7: [1, 7] Factors of 8: [1, 2, 4, 8] Factors of 9: [1, 3, 9] Factors of 10: [1, 2, 5, 10] Factors of 20: [1, 2, 4, 5, 10, 20] Factors of 40: [1, 2, 4, 5, 8, 10, 20, 40] Factors of 60: [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] Factors of 80: [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] Factors of 100: [1, 2, 4, 5, 10, 20, 25, 50, 100] Factors of 200: [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200] Factors of 300: [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300] Factors of 400: [1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400] Factors of 512: [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] Factors of 677: [1, 677] Factors of 768: [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768] Factors of 966: [1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966] Factors of 1000: [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000] Factors of 1024: [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024] Factors of 2048: [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048] Factors of 4096: [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096]
GAP
# Built-in function
DivisorsInt(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]
# A possible implementation, not suitable to large n
div := n -> Filtered([1 .. n], k -> n mod k = 0);
div(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]
# Another implementation, usable for large n (if n can be factored quickly)
div2 := function(n)
local f, p;
f := Collected(FactorsInt(n));
p := List(f, v -> List([0 .. v[2]], k -> v[1]^k));
return SortedList(List(Cartesian(p), Product));
end;
div2(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]
Go
Trial division, no prime number generator, but with some optimizations. It's good enough to factor any 64 bit integer, with large primes taking several seconds.
package main
import "fmt"
func main() {
printFactors(-1)
printFactors(0)
printFactors(1)
printFactors(2)
printFactors(3)
printFactors(53)
printFactors(45)
printFactors(64)
printFactors(600851475143)
printFactors(999999999999999989)
}
func printFactors(nr int64) {
if nr < 1 {
fmt.Println("\nFactors of", nr, "not computed")
return
}
fmt.Printf("\nFactors of %d: ", nr)
fs := make([]int64, 1)
fs[0] = 1
apf := func(p int64, e int) {
n := len(fs)
for i, pp := 0, p; i < e; i, pp = i+1, pp*p {
for j := 0; j < n; j++ {
fs = append(fs, fs[j]*pp)
}
}
}
e := 0
for ; nr & 1 == 0; e++ {
nr >>= 1
}
apf(2, e)
for d := int64(3); nr > 1; d += 2 {
if d*d > nr {
d = nr
}
for e = 0; nr%d == 0; e++ {
nr /= d
}
if e > 0 {
apf(d, e)
}
}
fmt.Println(fs)
fmt.Println("Number of factors =", len(fs))
}
- Output:
Factors of -1 not computed Factors of 0 not computed Factors of 1: [1] Number of factors = 1 Factors of 2: [1 2] Number of factors = 2 Factors of 3: [1 3] Number of factors = 2 Factors of 53: [1 53] Number of factors = 2 Factors of 45: [1 3 9 5 15 45] Number of factors = 6 Factors of 64: [1 2 4 8 16 32 64] Number of factors = 7 Factors of 600851475143: [1 71 839 59569 1471 104441 1234169 87625999 6857 486847 5753023 408464633 10086647 716151937 8462696833 600851475143] Number of factors = 16 Factors of 999999999999999989: [1 999999999999999989] Number of factors = 2
Gosu
var numbers = {11, 21, 32, 45, 67, 96}
numbers.each(\ number -> printFactors(number))
function printFactors(n: int) {
if (n < 1) return
var result ="${n} => "
(1 .. n/2).each(\ i -> {result += n % i == 0 ? "${i} " : ""})
print("${result}${n}")
}
- Output:
11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 16 32 45 => 1 3 5 9 15 45 67 => 1 67 96 => 1 2 3 4 6 8 12 16 24 32 48 96
Groovy
A straight brute force approach up to the square root of N:
def factorize = { long target ->
if (target == 1) return [1L]
if (target < 4) return [1L, target]
def targetSqrt = Math.sqrt(target)
def lowfactors = (2L..targetSqrt).grep { (target % it) == 0 }
if (lowfactors == []) return [1L, target]
def nhalf = lowfactors.size() - ((lowfactors[-1] == targetSqrt) ? 1 : 0)
[1] + lowfactors + (0..<nhalf).collect { target.intdiv(lowfactors[it]) }.reverse() + [target]
}
Test:
((1..30) + [333333]).each { println ([number:it, factors:factorize(it)]) }
- Output:
[number:1, factors:[1]] [number:2, factors:[1, 2]] [number:3, factors:[1, 3]] [number:4, factors:[1, 2, 4]] [number:5, factors:[1, 5]] [number:6, factors:[1, 2, 3, 6]] [number:7, factors:[1, 7]] [number:8, factors:[1, 2, 4, 8]] [number:9, factors:[1, 3, 9]] [number:10, factors:[1, 2, 5, 10]] [number:11, factors:[1, 11]] [number:12, factors:[1, 2, 3, 4, 6, 12]] [number:13, factors:[1, 13]] [number:14, factors:[1, 2, 7, 14]] [number:15, factors:[1, 3, 5, 15]] [number:16, factors:[1, 2, 4, 8, 16]] [number:17, factors:[1, 17]] [number:18, factors:[1, 2, 3, 6, 9, 18]] [number:19, factors:[1, 19]] [number:20, factors:[1, 2, 4, 5, 10, 20]] [number:21, factors:[1, 3, 7, 21]] [number:22, factors:[1, 2, 11, 22]] [number:23, factors:[1, 23]] [number:24, factors:[1, 2, 3, 4, 6, 8, 12, 24]] [number:25, factors:[1, 5, 25]] [number:26, factors:[1, 2, 13, 26]] [number:27, factors:[1, 3, 9, 27]] [number:28, factors:[1, 2, 4, 7, 14, 28]] [number:29, factors:[1, 29]] [number:30, factors:[1, 2, 3, 5, 6, 10, 15, 30]] [number:333333, factors:[1, 3, 7, 9, 11, 13, 21, 33, 37, 39, 63, 77, 91, 99, 111, 117, 143, 231, 259, 273, 333, 407, 429, 481, 693, 777, 819, 1001, 1221, 1287, 1443, 2331, 2849, 3003, 3367, 3663, 4329, 5291, 8547, 9009, 10101, 15873, 25641, 30303, 37037, 47619, 111111, 333333]]
Haskell
Using D. Amos'es Primes module for finding prime factors
import HFM.Primes (primePowerFactors)
import Control.Monad (mapM)
import Data.List (product)
-- primePowerFactors :: Integer -> [(Integer,Int)]
factors = map product .
mapM (\(p,m)-> [p^i | i<-[0..m]]) . primePowerFactors
Returns list of factors out of order, e.g.:
~> factors 42
[1,7,3,21,2,14,6,42]
Or, prime decomposition task can be used (although, a trial division-only version will become very slow for large primes),
import Data.List (group)
primePowerFactors = map (\x-> (head x, length x)) . group . factorize
The above function can also be found in the package arithmoi, as Math.NumberTheory.Primes.factorise :: Integer -> [(Integer, Int)], which performs "factorisation of Integers by the elliptic curve algorithm after Montgomery" and "is best suited for numbers of up to 50-60 digits".
Or, deriving cofactors from factors up to the square root:
integerFactors :: Int -> [Int]
integerFactors n
| 1 > n = []
| otherwise = lows <> (quot n <$> part n (reverse lows))
where
part n
| n == square = tail
| otherwise = id
(square, lows) =
(,) . (^ 2)
<*> (filter ((0 ==) . rem n) . enumFromTo 1)
$ floor (sqrt $ fromIntegral n)
main :: IO ()
main = print $ integerFactors 600
- Output:
[1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600]
List comprehension
Naive, functional, no import, in increasing order:
factorsNaive n =
[ i
| i <- [1 .. n]
, mod n i == 0 ]
~> factorsNaive 25
[1,5,25]
Factor, cofactor. Get the list of factor–cofactor pairs sorted, for a quadratic speedup:
import Data.List (sort)
factorsCo n =
sort
[ i
| i <- [1 .. floor (sqrt (fromIntegral n))]
, (d, 0) <- [divMod n i]
, i <-
i :
[ d
| d > i ] ]
A version of the above without the need for sorting, making it to be online (i.e. productive immediately, which can be seen in GHCi); factors in increasing order:
factorsO n =
ds ++
[ r
| (d, 0) <- [divMod n r]
, r <-
r :
[ d
| d > r ] ] ++
reverse (map (n `div`) ds)
where
r = floor (sqrt (fromIntegral n))
ds =
[ i
| i <- [1 .. r - 1]
, mod n i == 0 ]
Testing:
*Main> :set +s
~> factorsO 120
[1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120]
(0.00 secs, 0 bytes)
~> factorsO 12041111117
[1,7,41,287,541,3787,22181,77551,155267,542857,3179591,22257137,41955091,2936856
37,1720158731,12041111117]
(0.09 secs, 50758224 bytes)
HicEst
DLG(NameEdit=N, TItle='Enter an integer')
DO i = 1, N^0.5
IF( MOD(N,i) == 0) WRITE() i, N/i
ENDDO
ENDIcon and Unicon
- Output:
factors of 32767=1 7 31 151 217 1057 4681 32767 factors of 45=1 3 5 9 15 45 factors of 53=1 53 factors of 64=1 2 4 8 16 32 64 factors of 100=1 2 4 5 10 20 25 50 100
Insitux
(function factors n
(filter (div? n) (range 1 (inc n))))
(factors 45)- Output:
[1 3 5 9 15 45]
J
The "brute force" approach is the most concise:
foi=: [: I. 0 = (|~ i.@>:)
Example use:
foi 40
1 2 4 5 8 10 20 40
Basically we test every non-negative integer up through the number itself to see if it divides evenly.
However, this becomes very slow for large numbers. So other approaches can be worthwhile.
J has a primitive, q: which returns its argument's prime factors.
q: 40
2 2 2 5
Alternatively, q: can produce provide a table of the exponents of the unique relevant prime factors
__ q: 420
2 3 5 7
2 1 1 1
With this, we can form lists of each of the potential relevant powers of each of these prime factors
(^ i.@>:)&.>/ __ q: 420
┌─────┬───┬───┬───┐
│1 2 4│1 3│1 5│1 7│
└─────┴───┴───┴───┘
From here, it's a simple matter (*/&>@{ or, find all possible combinations of one item from each list ({ without a left argument) then unpack each list and multiply its elements) to compute all possible factors of the original number
factrs=: */&>@{@((^ i.@>:)&.>/)@q:~&__
factrs 40
1 5
2 10
4 20
8 40
However, a data structure which is organized around the prime decomposition of the argument can be hard to read. So, for reader convenience, we should probably arrange them in a monotonically increasing list:
factrst=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__
factrst 420
1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 140 210 420A less efficient, but concise variation on this theme:
~.,*/&> { 1 ,&.> q: 40
1 5 2 10 4 20 8 40This computes 2^n intermediate values where n is the number of prime factors of the original number.
That said, note that we get a representation issue when dealing with large numbers:
factors 568474220
1 2 4 5 10 17 20 34 68 85 170 340 1.67198e6 3.34397e6 6.68793e6 8.35992e6 1.67198e7 2.84237e7 3.34397e7 5.68474e7 1.13695e8 1.42119e8 2.84237e8 5.68474e8One approach here (if we don't want to explicitly format the result) is to use an arbitrary precision (aka "extended") argument. This propagates through into the result:
factors 568474220x
1 2 4 5 10 17 20 34 68 85 170 340 1671983 3343966 6687932 8359915 16719830 28423711 33439660 56847422 113694844 142118555 284237110 568474220Another less efficient approach, in which remainders are examined up to the square root, larger factors obtained as fractions, and the combined list nubbed and sorted might be:
factorsOfNumber=: monad define
Y=. y"_
/:~ ~. ( , Y%]) ( #~ 0=]|Y) 1+i.>.%:y
)
factorsOfNumber 40
1 2 4 5 8 10 20 40Another approach:
odometer =: #: i.@(*/)
factors=: (*/@:^"1 odometer@:>:)/@q:~&__See also the J essays Odometer and Divisors.
Java
public static TreeSet<Long> factors(long n)
{
TreeSet<Long> factors = new TreeSet<Long>();
factors.add(n);
factors.add(1L);
for(long test = n - 1; test >= Math.sqrt(n); test--)
if(n % test == 0)
{
factors.add(test);
factors.add(n / test);
}
return factors;
}JavaScript
Imperative
function factors(num)
{
var
n_factors = [],
i;
for (i = 1; i <= Math.floor(Math.sqrt(num)); i += 1)
if (num % i === 0)
{
n_factors.push(i);
if (num / i !== i)
n_factors.push(num / i);
}
n_factors.sort(function(a, b){return a - b;}); // numeric sort
return n_factors;
}
factors(45); // [1,3,5,9,15,45]
factors(53); // [1,53]
factors(64); // [1,2,4,8,16,32,64]Functional
ES5
Translating the naive list comprehension example from Haskell, using a list monad for the comprehension
// Monadic bind (chain) for lists
function chain(xs, f) {
return [].concat.apply([], xs.map(f));
}
// [m..n]
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
return m + i;
});
}
function factors_naive(n) {
return chain( range(1, n), function (x) { // monadic chain/bind
return n % x ? [] : [x]; // monadic fail or inject/return
});
}
factors_naive(6)Output:
[1, 2, 3, 6]Translating the Haskell (lows and highs) example
console.log(
(function (lstTest) {
// INTEGER FACTORS
function integerFactors(n) {
var rRoot = Math.sqrt(n),
intRoot = Math.floor(rRoot),
lows = range(1, intRoot).filter(function (x) {
return (n % x) === 0;
});
// for perfect squares, we can drop the head of the 'highs' list
return lows.concat(lows.map(function (x) {
return n / x;
}).reverse().slice((rRoot === intRoot) | 0));
}
// [m .. n]
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
return m + i;
});
}
/*************************** TESTING *****************************/
// TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS
function alignedTable(lstRows, lngPad, fnAligned) {
var lstColWidths = range(0, lstRows.reduce(function (a, x) {
return x.length > a ? x.length : a;
}, 0) - 1).map(function (iCol) {
return lstRows.reduce(function (a, lst) {
var w = lst[iCol] ? lst[iCol].toString().length : 0;
return (w > a) ? w : a;
}, 0);
});
return lstRows.map(function (lstRow) {
return lstRow.map(function (v, i) {
return fnAligned(v, lstColWidths[i] + lngPad);
}).join('')
}).join('\n');
}
function alignRight(n, lngWidth) {
var s = n.toString();
return Array(lngWidth - s.length + 1).join(' ') + s;
}
// TEST
return '\nintegerFactors(n)\n\n' + alignedTable(
lstTest.map(integerFactors).map(function (x, i) {
return [lstTest[i], '-->'].concat(x);
}), 2, alignRight
) + '\n';
})([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767])
);Output:
integerFactors(n)
25 --> 1 5 25
45 --> 1 3 5 9 15 45
53 --> 1 53
64 --> 1 2 4 8 16 32 64
100 --> 1 2 4 5 10 20 25 50 100
102 --> 1 2 3 6 17 34 51 102
120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
12345 --> 1 3 5 15 823 2469 4115 12345
32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766
32767 --> 1 7 31 151 217 1057 4681 32767
ES6
(function (lstTest) {
'use strict';
// INTEGER FACTORS
// integerFactors :: Int -> [Int]
let integerFactors = (n) => {
let rRoot = Math.sqrt(n),
intRoot = Math.floor(rRoot),
lows = range(1, intRoot)
.filter(x => (n % x) === 0);
// for perfect squares, we can drop
// the head of the 'highs' list
return lows.concat(lows
.map(x => n / x)
.reverse()
.slice((rRoot === intRoot) | 0)
);
},
// range :: Int -> Int -> [Int]
range = (m, n) => Array.from({
length: (n - m) + 1
}, (_, i) => m + i);
/*************************** TESTING *****************************/
// TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS
let alignedTable = (lstRows, lngPad, fnAligned) => {
var lstColWidths = range(
0, lstRows
.reduce(
(a, x) => (x.length > a ? x.length : a),
0
) - 1
)
.map((iCol) => lstRows
.reduce((a, lst) => {
let w = lst[iCol] ? lst[iCol].toString()
.length : 0;
return (w > a) ? w : a;
}, 0));
return lstRows.map((lstRow) =>
lstRow.map((v, i) => fnAligned(
v, lstColWidths[i] + lngPad
))
.join('')
)
.join('\n');
},
alignRight = (n, lngWidth) => {
let s = n.toString();
return Array(lngWidth - s.length + 1)
.join(' ') + s;
};
// TEST
return '\nintegerFactors(n)\n\n' + alignedTable(lstTest
.map(integerFactors)
.map(
(x, i) => [lstTest[i], '-->'].concat(x)
), 2, alignRight
) + '\n';
})([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767]);- Output:
integerFactors(n)
25 --> 1 5 25
45 --> 1 3 5 9 15 45
53 --> 1 53
64 --> 1 2 4 8 16 32 64
100 --> 1 2 4 5 10 20 25 50 100
102 --> 1 2 3 6 17 34 51 102
120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
12345 --> 1 3 5 15 823 2469 4115 12345
32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766
32767 --> 1 7 31 151 217 1057 4681 32767
jq
# This implementation uses "sort" for tidiness
def factors:
. as $num
| reduce range(1; 1 + sqrt|floor) as $i
([];
if ($num % $i) == 0 then
($num / $i) as $r
| if $i == $r then . + [$i] else . + [$i, $r] end
else .
end )
| sort;
def task:
(45, 53, 64) | "\(.): \(factors)" ;
task- Output:
$ jq -n -M -r -c -f factors.jq 45: [1,3,5,9,15,45] 53: [1,53] 64: [1,2,4,8,16,32,64]
Julia
using Primes
""" Return the factors of n, including 1, n """
function factors(n::T)::Vector{T} where T <: Integer
sort(vec(map(prod, Iterators.product((p.^(0:m) for (p, m) in eachfactor(n))...))))
end
const examples = [28, 45, 53, 64, 6435789435768]
for n in examples
@time println("The factors of $n are: $(factors(n))")
end- Output:
The factors of 28 are: [1, 2, 4, 7, 14, 28] 0.330684 seconds (784.75 k allocations: 39.104 MiB, 3.17% gc time) The factors of 45 are: [1, 3, 5, 9, 15, 45] 0.000117 seconds (56 allocations: 2.672 KiB) The factors of 53 are: [1, 53] 0.000102 seconds (35 allocations: 1.516 KiB) The factors of 64 are: [1, 2, 4, 8, 16, 32, 64] 0.000093 seconds (56 allocations: 3.172 KiB) The factors of 6435789435768 are: [1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 191, 231, 264, 308, 382, 462, 573, 616, 764, 924, 1146, 1337, 1528, 1848, 2101, 2292, 2674, 4011, 4202, 4584, 5348, 6303, 8022, 8404, 10696, 12606, 14707, 16044, 16808, 25212, 29414, 32088, 44121, 50424, 58828, 88242, 117656, 176484, 352968, 18233351, 36466702, 54700053, 72933404, 109400106, 127633457, 145866808, 200566861, 218800212, 255266914, 382900371, 401133722, 437600424, 510533828, 601700583, 765800742, 802267444, 1021067656, 1203401166, 1403968027, 1531601484, 1604534888, 2406802332, 2807936054, 3063202968, 3482570041, 4211904081, 4813604664, 5615872108, 6965140082, 8423808162, 10447710123, 11231744216, 13930280164, 16847616324, 20895420246, 24377990287, 27860560328, 33695232648, 38308270451, 41790840492, 48755980574, 73133970861, 76616540902, 83581680984, 97511961148, 114924811353, 146267941722, 153233081804, 195023922296, 229849622706, 268157893157, 292535883444, 306466163608, 459699245412, 536315786314, 585071766888, 804473679471, 919398490824, 1072631572628, 1608947358942, 2145263145256, 3217894717884, 6435789435768] 0.000249 seconds (451 allocations: 24.813 KiB)
K
f:{i:{y[&x=y*x div y]}[x;1+!_sqrt x];?i,x div|i}
equivalent to:
q)f:{i:{y where x=y*x div y}[x ; 1+ til floor sqrt x]; distinct i,x div reverse i}
f 120
1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
f 1024
1 2 4 8 16 32 64 128 256 512 1024
f 600851475143
1 71 839 1471 6857 59569 104441 486847 1234169 5753023 10086647 87625999 408464633 716151937 8462696833 600851475143
#f 3491888400 / has 1920 factors
1920
/ Number of factors for 3491888400 .. 3491888409
#:'f' 3491888400+!10
1920 16 4 4 12 16 32 16 8 24Kotlin
fun printFactors(n: Int) {
if (n < 1) return
print("$n => ")
(1..n / 2)
.filter { n % it == 0 }
.forEach { print("$it ") }
println(n)
}
fun main(args: Array<String>) {
val numbers = intArrayOf(11, 21, 32, 45, 67, 96)
for (number in numbers) printFactors(number)
}- Output:
11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 16 32 45 => 1 3 5 9 15 45 67 => 1 67 96 => 1 2 3 4 6 8 12 16 24 32 48 96
Lambdatalk
{def factors
{def factors.r
{lambda {:num :i :N}
{if {> :i :N}
then
else {if {= {% :num :i} 0}
then :i
{if {not {= {/ :num :i} :i}}
then {/ :num :i}
else}
else}
{factors.r :num {+ :i 1} :N} }}}
{lambda {:n}
{S.sort < {factors.r :n 1 {sqrt :n}}}}}
-> factors
{factors 45}
-> 1 3 5 9 15 45
{factors 53}
-> 1 53
{factors 64}
-> 1 2 4 8 16 32 64LFE
Using List Comprehensions
This following function is elegant looking and concise. However, it will not handle large numbers well: it will consume a great deal of memory (on one large number, the function consumed 4.3GB of memory on my desktop machine):
(defun factors (n)
(list-comp
((<- i (when (== 0 (rem n i))) (lists:seq 1 (trunc (/ n 2)))))
i))Non-Stack-Consuming
This version will not consume the stack (this function only used 18MB of memory on my machine with a ridiculously large number):
(defun factors (n)
"Tail-recursive prime factors function."
(factors n 2 '()))
(defun factors
((1 _ acc) (++ acc '(1)))
((n _ acc) (when (=< n 0))
#(error undefined))
((n k acc) (when (== 0 (rem n k)))
(factors (div n k) k (cons k acc)))
((n k acc)
(factors n (+ k 1) acc)))- Output:
> (factors 10677106534462215678539721403561279) (104729 104729 104729 98731 98731 32579 29269 1)
Lingo
on factors(n)
res = [1]
repeat with i = 2 to n/2
if n mod i = 0 then res.add(i)
end repeat
res.add(n)
return res
endput factors(45)
-- [1, 3, 5, 9, 15, 45]
put factors(53)
-- [1, 53]
put factors(64)
-- [1, 2, 4, 8, 16, 32, 64]Logo
to factors :n
output filter [equal? 0 modulo :n ?] iseq 1 :n
end
show factors 28 ; [1 2 4 7 14 28]Lua
function Factors( n )
local f = {}
for i = 1, n/2 do
if n % i == 0 then
f[#f+1] = i
end
end
f[#f+1] = n
return f
endM2000 Interpreter
\\ Factors of an integer
\\ For act as BASIC's FOR (if N<1 no loop start)
FORM 60,40
SET SWITCHES "+FOR"
MODULE LikeBasic {
10 INPUT N%
20 FOR I%=1 TO N%
30 IF N%/I%=INT(N%/I%) THEN PRINT I%,
40 NEXT I%
50 PRINT
}
CALL LikeBasic
SET SWITCHES "-FOR"
MODULE LikeM2000 {
DEF DECIMAL N%, I%
INPUT N%
IF N%<1 THEN EXIT
FOR I%=1 TO N% {
IF N% MOD I%=0 THEN PRINT I%,
}
PRINT
}
CALL LikeM2000Maple
numtheory:-divisors(n);Mathematica / Wolfram Language
Factorize[n_Integer] := Divisors[n]MATLAB / Octave
function fact(n);
f = factor(n); % prime decomposition
K = dec2bin(0:2^length(f)-1)-'0'; % generate all possible permutations
F = ones(1,2^length(f));
for k = 1:size(K)
F(k) = prod(f(~K(k,:))); % and compute products
end;
F = unique(F); % eliminate duplicates
printf('There are %i factors for %i.\n',length(F),n);
disp(F);
end;- Output:
>> fact(12)
There are 6 factors for 12.
1 2 3 4 6 12
>> fact(28)
There are 6 factors for 28.
1 2 4 7 14 28
>> fact(64)
There are 7 factors for 64.
1 2 4 8 16 32 64
>>fact(53)
There are 2 factors for 53.
1 53
Maxima
The builtin divisors function does this.
(%i96) divisors(100);
(%o96) {1,2,4,5,10,20,25,50,100}Such a function could be implemented like so:
divisors2(n) := map( lambda([l], lreduce("*", l)),
apply( cartesian_product,
map( lambda([fac],
setify(makelist(fac[1]^i, i, 0, fac[2]))),
ifactors(n))));MAXScript
fn factors n =
(
return (for i = 1 to n+1 where mod n i == 0 collect i)
)- Output:
factors 3
#(1, 3)
factors 7
#(1, 7)
factors 14
#(1, 2, 7, 14)
factors 60
#(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
factors 54
#(1, 2, 3, 6, 9, 18, 27, 54)Mercury
Mercury is both a logic language and a functional language. As such there are two possible interfaces for calculating the factors of an integer. This code shows both styles of implementation. Note that much of the code here is ceremony put in place to have this be something which can actually compile. The actual factoring is contained in the predicate factor/2 and in the function factor/1. The function form is implemented in terms of the predicate form rather than duplicating all of the predicate code.
The predicates main/2 and factor/2 are shown with the combined type and mode statement (e.g. int::in) as is the usual case for simple predicates with only one mode. This makes the code more immediately understandable. The predicate factor/5, however, has its mode broken out onto a separate line both to show Mercury's mode statement (useful for predicates which can have varying instantiation of parameters) and to stop the code from extending too far to the right. Finally the function factor/1 has its mode statements removed (shown underneath in a comment for illustration purposes) because good coding style (and the default of the compiler!) has all parameters "in"-moded and the return value "out"-moded.
This implementation of factoring works as follows:
- The input number itself and 1 are both considered factors.
- The numbers between 2 and the square root of the input number are checked for even division.
- If the incremental number divides evenly into the input number, both the incremental number and the quotient are added to the list of factors.
This implementation makes use of Mercury's "state variable notation" to keep a pair of variables for accumulation, thus allowing the implementation to be tail recursive. !Accumulator is syntax sugar for a *pair* of variables. One of them is an "in"-moded variable and the other is an "out"-moded variable. !:Accumulator is the "out" portion and !.Accumulator is the "in" portion in the ensuing code.
Using the state variable notation avoids having to keep track of strings of variables unified in the code named things like Acc0, Acc1, Acc2, Acc3, etc.
fac.m
:- module fac.
:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.
:- implementation.
:- import_module float, int, list, math, string.
main(!IO) :-
io.command_line_arguments(Args, !IO),
list.filter_map(string.to_int, Args, CleanArgs),
list.foldl((pred(Arg::in, !.IO::di, !:IO::uo) is det :-
factor(Arg, X),
io.format("factor(%d, [", [i(Arg)], !IO),
io.write_list(X, ",", io.write_int, !IO),
io.write_string("])\n", !IO)
), CleanArgs, !IO).
:- pred factor(int::in, list(int)::out) is det.
factor(N, Factors) :-
Limit = float.truncate_to_int(math.sqrt(float(N))),
factor(N, 2, Limit, [], Unsorted),
list.sort_and_remove_dups([1, N | Unsorted], Factors).
:- pred factor(int, int, int, list(int), list(int)).
:- mode factor(in, in, in, in, out) is det.
factor(N, X, Limit, !Accumulator) :-
( if X > Limit
then true
else ( if 0 = N mod X
then !:Accumulator = [X, N / X | !.Accumulator]
else true ),
factor(N, X + 1, Limit, !Accumulator) ).
:- func factor(int) = list(int).
%:- mode factor(in) = out is det.
factor(N) = Factors :- factor(N, Factors).
:- end_module fac.Use and output
Use of the code looks like this:
$ mmc fac.m && ./fac 100 999 12345678 booger factor(100, [1,2,4,5,10,20,25,50,100]) factor(999, [1,3,9,27,37,111,333,999]) factor(12345678, [1,2,3,6,9,18,47,94,141,282,423,846,14593,29186,43779,87558,131337,262674,685871,1371742,2057613,4115226,6172839,12345678])
min
(mod 0 ==) :divisor?
(() 0 shorten) :new
(new (over swons 'pred dip) pick times nip) :iota
(
:n
n sqrt int iota ; Only consider numbers up to sqrt(n).
(n swap divisor?) filter =f1
f1 (n swap div) map reverse =f2 ; "Mirror" the list of divisors at sqrt(n).
(f1 last f2 first ==) (f2 rest #f2) when ; Handle perfect squares.
f1 f2 concat
) :factors
24 factors puts!
9 factors puts!
11 factors puts!MiniScript
factors = function(n)
result = [1]
for i in range(2, n)
if n % i == 0 then result.push i
end for
return result
end function
while true
n = val(input("Number to factor (0 to quit)? "))
if n <= 0 then break
print factors(n)
end while- Output:
Number to factor (0 to quit)? 42 [1, 2, 3, 6, 7, 14, 21, 42] Number to factor (0 to quit)? 101 [1, 101] Number to factor (0 to quit)? 360 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360] Number to factor (0 to quit)? 0
МК-61/52
П9 1 П6 КИП6 ИП9 ИП6 / П8 ^ [x] x#0 21 - x=0 03 ИП6 С/П ИП8 П9 БП 04 1 С/П БП 21
MUMPS
factors(num) New fctr,list,sep,sqrt
If num<1 Quit "Too small a number"
If num["." Quit "Not an integer"
Set sqrt=num**0.5\1
For fctr=1:1:sqrt Set:num/fctr'["." list(fctr)=1,list(num/fctr)=1
Set (list,fctr)="",sep="[" For Set fctr=$Order(list(fctr)) Quit:fctr="" Set list=list_sep_fctr,sep=","
Quit list_"]"
w $$factors(45) ; [1,3,5,9,15,45]
w $$factors(53) ; [1,53]
w $$factors(64) ; [1,2,4,8,16,32,64]Nanoquery
n = int(input())
for i in range(1, n / 2)
if (n % i = 0)
print i + " "
end
end
println nNetRexx
/* NetRexx ***********************************************************
* 21.04.2013 Walter Pachl
* 21.04.2013 add method main to accept argument(s)
*********************************************************************/
options replace format comments java crossref symbols nobinary
class divl
method main(argwords=String[]) static
arg=Rexx(argwords)
Parse arg a b
Say a b
If a='' Then Do
help='java divl low [high] shows'
help=help||' divisors of all numbers between low and high'
Say help
Return
End
If b='' Then b=a
loop x=a To b
say x '->' divs(x)
End
method divs(x) public static returns Rexx
if x==1 then return 1 /*handle special case of 1 */
lo=1
hi=x
odd=x//2 /* 1 if x is odd */
loop j=2+odd By 1+odd While j*j<x /*divide by numbers<sqrt(x) */
if x//j==0 then Do /*Divisible? Add two divisors:*/
lo=lo j /* list low divisors */
hi=x%j hi /* list high divisors */
End
End
If j*j=x Then /*for a square number as input */
lo=lo j /* add its square root */
return lo hi /* return both lists */- Output:
java divl 1 10 1 -> 1 2 -> 1 2 3 -> 1 3 4 -> 1 2 4 5 -> 1 5 6 -> 1 2 3 6 7 -> 1 7 8 -> 1 2 4 8 9 -> 1 3 9 10 -> 1 2 5 10
Nim
import intsets, math, algorithm
proc factors(n: int): seq[int] =
var fs: IntSet
for x in 1 .. int(sqrt(float(n))):
if n mod x == 0:
fs.incl(x)
fs.incl(n div x)
for x in fs:
result.add(x)
result.sort()
echo factors(45)Niue
[ 'n ; [ negative-or-zero [ , ] if
[ n not-factor [ , ] when ] else ] n times n ] 'factors ;
[ dup 0 <= ] 'negative-or-zero ;
[ swap dup rot swap mod 0 = not ] 'not-factor ;
( tests )
100 factors .s .clr ( => 1 2 4 5 10 20 25 50 100 ) newline
53 factors .s .clr ( => 1 53 ) newline
64 factors .s .clr ( => 1 2 4 8 16 32 64 ) newline
12 factors .s .clr ( => 1 2 3 4 6 12 )Oberon-2
Oxford Oberon-2
MODULE Factors;
IMPORT Out,SYSTEM;
TYPE
LIPool = POINTER TO ARRAY OF LONGINT;
LIVector= POINTER TO LIVectorDesc;
LIVectorDesc = RECORD
cap: INTEGER;
len: INTEGER;
LIPool: LIPool;
END;
PROCEDURE New(cap: INTEGER): LIVector;
VAR
v: LIVector;
BEGIN
NEW(v);
v.cap := cap;
v.len := 0;
NEW(v.LIPool,cap);
RETURN v
END New;
PROCEDURE (v: LIVector) Add(x: LONGINT);
VAR
newLIPool: LIPool;
BEGIN
IF v.len = LEN(v.LIPool^) THEN
(* run out of space *)
v.cap := v.cap + (v.cap DIV 2);
NEW(newLIPool,v.cap);
SYSTEM.MOVE(SYSTEM.ADR(v.LIPool^),SYSTEM.ADR(newLIPool^),v.cap * SIZE(LONGINT));
v.LIPool := newLIPool
END;
v.LIPool[v.len] := x;
INC(v.len)
END Add;
PROCEDURE (v: LIVector) At(idx: INTEGER): LONGINT;
BEGIN
RETURN v.LIPool[idx];
END At;
PROCEDURE Factors(n:LONGINT): LIVector;
VAR
j: LONGINT;
v: LIVector;
BEGIN
v := New(16);
FOR j := 1 TO n DO
IF (n MOD j) = 0 THEN v.Add(j) END;
END;
RETURN v
END Factors;
VAR
v: LIVector;
j: INTEGER;
BEGIN
v := Factors(123);
FOR j := 0 TO v.len - 1 DO
Out.LongInt(v.At(j),4);Out.Ln
END;
Out.Int(v.len,6);Out.String(" factors");Out.Ln
END Factors.- Output:
1
3
41
123
4 factors
Objeck
use IO;
use Structure;
bundle Default {
class Basic {
function : native : GenerateFactors(n : Int) ~ IntVector {
factors := IntVector->New();
factors-> AddBack(1);
factors->AddBack(n);
for(i := 2; i * i <= n; i += 1;) {
if(n % i = 0) {
factors->AddBack(i);
if(i * i <> n) {
factors->AddBack(n / i);
};
};
};
factors->Sort();
return factors;
}
function : Main(args : String[]) ~ Nil {
numbers := [3135, 45, 60, 81];
for(i := 0; i < numbers->Size(); i += 1;) {
factors := GenerateFactors(numbers[i]);
Console->GetInstance()->Print("Factors of ")->Print(numbers[i])->PrintLine(" are:");
each(i : factors) {
Console->GetInstance()->Print(factors->Get(i))->Print(", ");
};
"\n\n"->Print();
};
}
}
}OCaml
let rec range = function 0 -> [] | n -> range(n-1) @ [n]
let factors n =
List.filter (fun v -> (n mod v) = 0) (range n)Odin
Uses built-in dynamic arrays, and only checks up to the square root
package main
import "core:fmt"
import "core:slice"
factors :: proc(n: int) -> [dynamic]int {
d := 1
factors := make([dynamic]int)
for {
q := n / d
r := n % d
if d >= q {
if d == q && r == 0 {
append(&factors, d)
}
slice.sort(factors[:])
return factors
}
if r == 0 {
append(&factors, d, q)
}
d += 1
}
}
main :: proc() {
for n in ([?]int{100, 108, 999, 255, 256, 257}) {
a := factors(n)
fmt.println("The factors of", n, "are", a)
delete(a)
}
}- Output:
The factors of 100 are [1, 2, 4, 5, 10, 20, 25, 50, 100] The factors of 108 are [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108] The factors of 999 are [1, 3, 9, 27, 37, 111, 333, 999] The factors of 255 are [1, 3, 5, 15, 17, 51, 85, 255] The factors of 256 are [1, 2, 4, 8, 16, 32, 64, 128, 256] The factors of 257 are [1, 257]
Oforth
Integer method: factors self seq filter(#[ self isMultiple ]) ;
120 factors println- Output:
[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]
Oz
declare
fun {Factors N}
Sqr = {Float.toInt {Sqrt {Int.toFloat N}}}
Fs = for X in 1..Sqr append:App do
if N mod X == 0 then
CoFactor = N div X
in
if CoFactor == X then %% avoid duplicate factor
{App [X]} %% when N is a square number
else
{App [X CoFactor]}
end
end
end
in
{Sort Fs Value.'<'}
end
in
{Show {Factors 53}}Panda
Panda has a factor function already, it's defined as:
fun factor(n) type integer->integer
f where n.mod(1..n=>f)==0
45.factorPARI/GP
divisors(n)Pascal
program Factors;
var
i, number: integer;
begin
write('Enter a number between 1 and 2147483647: ');
readln(number);
for i := 1 to round(sqrt(number)) - 1 do
if number mod i = 0 then
write (i, ' ', number div i, ' ');
// Check to see if number is a square
i := round(sqrt(number));
if i*i = number then
write(i)
else if number mod i = 0 then
write(i, number/i);
writeln;
end.- Output:
Enter a number between 1 and 2147483647: 49 1 49 7 Enter a number between 1 and 2147483647: 353435 1 25755 3 8585 5 5151 15 1717 17 1515 51 505 85 303 101 255
using Prime decomposition
like [C Prime_factoring].
Insertion sort was much faster, because mostly not so many factors need to be sorted.
"runtime overhead" +25% instead +100% for quicksort against no sort.
Especially fast for consecutive integers.
program FacOfInt;
// gets factors of consecutive integers fast
// limited to 1.2e11
{$IFDEF FPC}
{$MODE DELPHI} {$OPTIMIZATION ON,ALL} {$COPERATORS ON}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
uses
sysutils
{$IFDEF WINDOWS},Windows{$ENDIF}
;
//######################################################################
//prime decomposition
const
//HCN(86) > 1.2E11 = 128,501,493,120 count of divs = 4096 7 3 1 1 1 1 1 1 1
HCN_DivCnt = 4096;
type
tItem = Uint64;
tDivisors = array [0..HCN_DivCnt] of tItem;
tpDivisor = pUint64;
const
//used odd size for test only
SizePrDeFe = 32768;//*72 <= 64kb level I or 2 Mb ~ level 2 cache
type
tdigits = array [0..31] of Uint32;
//the first number with 11 different prime factors =
//2*3*5*7*11*13*17*19*23*29*31 = 2E11
//56 byte
tprimeFac = packed record
pfSumOfDivs,
pfRemain : Uint64;
pfDivCnt : Uint32;
pfMaxIdx : Uint32;
pfpotPrimIdx : array[0..9] of word;
pfpotMax : array[0..11] of byte;
end;
tpPrimeFac = ^tprimeFac;
tPrimeDecompField = array[0..SizePrDeFe-1] of tprimeFac;
tPrimes = array[0..65535] of Uint32;
var
{$ALIGN 8}
SmallPrimes: tPrimes;
{$ALIGN 32}
PrimeDecompField :tPrimeDecompField;
pdfIDX,pdfOfs: NativeInt;
procedure InitSmallPrimes;
//get primes. #0..65535.Sieving only odd numbers
const
MAXLIMIT = (821641-1) shr 1;
var
pr : array[0..MAXLIMIT] of byte;
p,j,d,flipflop :NativeUInt;
Begin
SmallPrimes[0] := 2;
fillchar(pr[0],SizeOf(pr),#0);
p := 0;
repeat
repeat
p +=1
until pr[p]= 0;
j := (p+1)*p*2;
if j>MAXLIMIT then
BREAK;
d := 2*p+1;
repeat
pr[j] := 1;
j += d;
until j>MAXLIMIT;
until false;
SmallPrimes[1] := 3;
SmallPrimes[2] := 5;
j := 3;
d := 7;
flipflop := (2+1)-1;//7+2*2,11+2*1,13,17,19,23
p := 3;
repeat
if pr[p] = 0 then
begin
SmallPrimes[j] := d;
inc(j);
end;
d += 2*flipflop;
p+=flipflop;
flipflop := 3-flipflop;
until (p > MAXLIMIT) OR (j>High(SmallPrimes));
end;
function OutPots(pD:tpPrimeFac;n:NativeInt):Ansistring;
var
s: String[31];
chk,p,i: NativeInt;
Begin
str(n,s);
result := s+' :';
with pd^ do
begin
str(pfDivCnt:3,s);
result += s+' : ';
chk := 1;
For n := 0 to pfMaxIdx-1 do
Begin
if n>0 then
result += '*';
p := SmallPrimes[pfpotPrimIdx[n]];
chk *= p;
str(p,s);
result += s;
i := pfpotMax[n];
if i >1 then
Begin
str(pfpotMax[n],s);
result += '^'+s;
repeat
chk *= p;
dec(i);
until i <= 1;
end;
end;
p := pfRemain;
If p >1 then
Begin
str(p,s);
chk *= p;
result += '*'+s;
end;
str(chk,s);
result += '_chk_'+s+'<';
str(pfSumOfDivs,s);
result += '_SoD_'+s+'<';
end;
end;
function smplPrimeDecomp(n:Uint64):tprimeFac;
var
pr,i,pot,fac,q :NativeUInt;
Begin
with result do
Begin
pfDivCnt := 1;
pfSumOfDivs := 1;
pfRemain := n;
pfMaxIdx := 0;
pfpotPrimIdx[0] := 1;
pfpotMax[0] := 0;
i := 0;
while i < High(SmallPrimes) do
begin
pr := SmallPrimes[i];
q := n DIV pr;
//if n < pr*pr
if pr > q then
BREAK;
if n = pr*q then
Begin
pfpotPrimIdx[pfMaxIdx] := i;
pot := 0;
fac := pr;
repeat
n := q;
q := n div pr;
pot+=1;
fac *= pr;
until n <> pr*q;
pfpotMax[pfMaxIdx] := pot;
pfDivCnt *= pot+1;
pfSumOfDivs *= (fac-1)DIV(pr-1);
inc(pfMaxIdx);
end;
inc(i);
end;
pfRemain := n;
if n > 1 then
Begin
pfDivCnt *= 2;
pfSumOfDivs *= n+1
end;
end;
end;
function CnvtoBASE(var dgt:tDigits;n:Uint64;base:NativeUint):NativeInt;
//n must be multiple of base aka n mod base must be 0
var
q,r: Uint64;
i : NativeInt;
Begin
fillchar(dgt,SizeOf(dgt),#0);
i := 0;
n := n div base;
result := 0;
repeat
r := n;
q := n div base;
r -= q*base;
n := q;
dgt[i] := r;
inc(i);
until (q = 0);
//searching lowest pot in base
result := 0;
while (result<i) AND (dgt[result] = 0) do
inc(result);
inc(result);
end;
function IncByBaseInBase(var dgt:tDigits;base:NativeInt):NativeInt;
var
q :NativeInt;
Begin
result := 0;
q := dgt[result]+1;
if q = base then
repeat
dgt[result] := 0;
inc(result);
q := dgt[result]+1;
until q <> base;
dgt[result] := q;
result +=1;
end;
function SieveOneSieve(var pdf:tPrimeDecompField):boolean;
var
dgt:tDigits;
i,j,k,pr,fac,n,MaxP : Uint64;
begin
n := pdfOfs;
if n+SizePrDeFe >= sqr(SmallPrimes[High(SmallPrimes)]) then
EXIT(FALSE);
//init
for i := 0 to SizePrDeFe-1 do
begin
with pdf[i] do
Begin
pfDivCnt := 1;
pfSumOfDivs := 1;
pfRemain := n+i;
pfMaxIdx := 0;
pfpotPrimIdx[0] := 0;
pfpotMax[0] := 0;
end;
end;
//first factor 2. Make n+i even
i := (pdfIdx+n) AND 1;
IF (n = 0) AND (pdfIdx<2) then
i := 2;
repeat
with pdf[i] do
begin
j := BsfQWord(n+i);
pfMaxIdx := 1;
pfpotPrimIdx[0] := 0;
pfpotMax[0] := j;
pfRemain := (n+i) shr j;
pfSumOfDivs := (Uint64(1) shl (j+1))-1;
pfDivCnt := j+1;
end;
i += 2;
until i >=SizePrDeFe;
//i now index in SmallPrimes
i := 0;
maxP := trunc(sqrt(n+SizePrDeFe))+1;
repeat
//search next prime that is in bounds of sieve
if n = 0 then
begin
repeat
inc(i);
pr := SmallPrimes[i];
k := pr-n MOD pr;
if k < SizePrDeFe then
break;
until pr > MaxP;
end
else
begin
repeat
inc(i);
pr := SmallPrimes[i];
k := pr-n MOD pr;
if (k = pr) AND (n>0) then
k:= 0;
if k < SizePrDeFe then
break;
until pr > MaxP;
end;
//no need to use higher primes
if pr*pr > n+SizePrDeFe then
BREAK;
//j is power of prime
j := CnvtoBASE(dgt,n+k,pr);
repeat
with pdf[k] do
Begin
pfpotPrimIdx[pfMaxIdx] := i;
pfpotMax[pfMaxIdx] := j;
pfDivCnt *= j+1;
fac := pr;
repeat
pfRemain := pfRemain DIV pr;
dec(j);
fac *= pr;
until j<= 0;
pfSumOfDivs *= (fac-1)DIV(pr-1);
inc(pfMaxIdx);
k += pr;
j := IncByBaseInBase(dgt,pr);
end;
until k >= SizePrDeFe;
until false;
//correct sum of & count of divisors
for i := 0 to High(pdf) do
Begin
with pdf[i] do
begin
j := pfRemain;
if j <> 1 then
begin
pfSumOFDivs *= (j+1);
pfDivCnt *=2;
end;
end;
end;
result := true;
end;
function NextSieve:boolean;
begin
dec(pdfIDX,SizePrDeFe);
inc(pdfOfs,SizePrDeFe);
result := SieveOneSieve(PrimeDecompField);
end;
function GetNextPrimeDecomp:tpPrimeFac;
begin
if pdfIDX >= SizePrDeFe then
if Not(NextSieve) then
EXIT(NIL);
result := @PrimeDecompField[pdfIDX];
inc(pdfIDX);
end;
function Init_Sieve(n:NativeUint):boolean;
//Init Sieve pdfIdx,pdfOfs are Global
begin
pdfIdx := n MOD SizePrDeFe;
pdfOfs := n-pdfIdx;
result := SieveOneSieve(PrimeDecompField);
end;
procedure InsertSort(pDiv:tpDivisor; Left, Right : NativeInt );
var
I, J: NativeInt;
Pivot : tItem;
begin
for i:= 1 + Left to Right do
begin
Pivot:= pDiv[i];
j:= i - 1;
while (j >= Left) and (pDiv[j] > Pivot) do
begin
pDiv[j+1]:=pDiv[j];
Dec(j);
end;
pDiv[j+1]:= pivot;
end;
end;
procedure GetDivisors(pD:tpPrimeFac;var Divs:tDivisors);
var
pDivs : tpDivisor;
pPot : UInt64;
i,len,j,l,p,k: Int32;
Begin
pDivs := @Divs[0];
pDivs[0] := 1;
len := 1;
l := 1;
with pD^ do
Begin
For i := 0 to pfMaxIdx-1 do
begin
//Multiply every divisor before with the new primefactors
//and append them to the list
k := pfpotMax[i];
p := SmallPrimes[pfpotPrimIdx[i]];
pPot :=1;
repeat
pPot *= p;
For j := 0 to len-1 do
Begin
pDivs[l]:= pPot*pDivs[j];
inc(l);
end;
dec(k);
until k<=0;
len := l;
end;
p := pfRemain;
If p >1 then
begin
For j := 0 to len-1 do
Begin
pDivs[l]:= p*pDivs[j];
inc(l);
end;
len := l;
end;
end;
//Sort. Insertsort much faster than QuickSort in this special case
InsertSort(pDivs,0,len-1);
//end marker
pDivs[len] :=0;
end;
procedure AllFacsOut(var Divs:tdivisors;proper:boolean=true);
var
k,j: Int32;
Begin
k := 0;
j := 1;
if Proper then
j:= 2;
repeat
IF Divs[j] = 0 then
BREAK;
write(Divs[k],',');
inc(j);
inc(k);
until false;
writeln(Divs[k]);
end;
var
pPrimeDecomp :tpPrimeFac;
Mypd : tPrimeFac;
Divs:tDivisors;
T0:Int64;
n : NativeUInt;
Begin
InitSmallPrimes;
T0 := GetTickCount64;
n := 0;
Init_Sieve(0);
repeat
pPrimeDecomp:= GetNextPrimeDecomp;
GetDivisors(pPrimeDecomp,Divs);
inc(n);
until n > 10*1000*1000+1;
T0 := GetTickCount64-T0;
writeln('runtime ',T0/1000:0:3,' s');
GetDivisors(pPrimeDecomp,Divs);
AllFacsOut(Divs,true);
AllFacsOut(Divs,false);
writeln('simple version');
T0 := GetTickCount64;
n := 0;
repeat
Mypd:= smplPrimeDecomp(n);
GetDivisors(@Mypd,Divs);
inc(n);
until n > 10*1000*1000+1;
T0 := GetTickCount64-T0;
writeln('runtime ',T0/1000:0:3,' s');
GetDivisors(@Mypd,Divs);
AllFacsOut(Divs,true);
AllFacsOut(Divs,false);
end.- Output:
TIO.RUN //out-commented GetDivisors, but still calculates sum of divisors and count of divisors runtime 0.555 s 1,11,909091 1,11,909091,10000001 simple version runtime 8.167 s 1,11,909091 1,11,909091,10000001 Real time: 8.868 s CPU share: 99.57 % //with GetDivisors runtime 1.815 s 1,11,909091 1,11,909091,10000001 simple version runtime 11.057 s 1,11,909091 1,11,909091,10000001 Real time: 13.082 s CPU share: 99.16 %
PascalABC.NET
function Factors(n: integer): List<integer>;
begin
var res := HSet(1,n);
for var i:=2 to n.Sqrt.Trunc do
if n.Divs(i) then
begin
res.Add(i);
res.Add(n div i);
end;
Result := res.Order.ToList;
end;
begin
foreach var x in |45,53,64| do
Println(x,Factors(x));
end.- Output:
45 [1,3,5,9,15,45] 53 [1,53] 64 [1,2,4,8,16,32,64]
Perl
sub factors
{
my($n) = @_;
return grep { $n % $_ == 0 }(1 .. $n);
}
print join ' ',factors(64), "\n";Or more intelligently:
sub factors {
my $n = shift;
$n = -$n if $n < 0;
my @divisors;
for (1 .. int(sqrt($n))) { # faster and less memory than map/grep
push @divisors, $_ unless $n % $_;
}
# Return divisors including top half, without duplicating a square
@divisors, map { $_*$_ == $n ? () : int($n/$_) } reverse @divisors;
}
print join " ", factors(64), "\n";One could also use a module, e.g.:
use ntheory qw/divisors/;
print join " ", divisors(12345678), "\n";
# Alternately something like: fordivisors { say } 12345678;Phix
There is a builtin factors(n), which takes an optional second parameter to include 1 and n:
?factors(12345,1)
- Output:
{1,3,5,15,823,2469,4115,12345}
You can find the implementation of factors(), prime_factors(), and prime_powers() in builtins\pfactors.e,
and mpz_factors(), mpz_prime_factors(), and mpz_pollard_rho() in mpfr.e for larger numbers, for example:
requires("1.0.2") -- [p2js/integer() bugs] include mpfr.e ?shorten(factors(3491888400),"factors",4) -- {2,3,4,5,"...",698377680,872972100,1163962800.0,1745944200.0," (1,918 factors)"} ?shorten(mpz_factors(3491888400),"factors",4) -- {2,3,4,5,"...",698377680,872972100,1163962800.0,1745944200.0," (1,918 factors)"} -- If the include1 parameter is 1 or "BOTH", then you'll also get 1 and 3491888400 ?prime_factors(3491888400) -- {2,3,5,7,11,13,17,19} ?prime_powers(3491888400) -- {{2,4},{3,3},{5,2},{7,1},{11,1},{13,1},{17,1},{19,1}} ?vslice(mpz_prime_factors("3491888400",10000),1) -- {2,3,5,7,11,13,17,19} ?mpz_prime_factors("3491888400",10000) -- {{2,4},{3,3},{5,2},{7,1},{11,1},{13,1},{17,1},{19,1}} -- Note that mpz_prime_factors() only accepts string or mpz, and not a raw native atom/integer. ?length(factors(108233175859200,1)) -- 666 ?length(mpz_factors(108233175859200,1)) -- 666 string d = "10677106534462215678539721403561279" ?mpz_prime_factors(d,10000) -- {{29269,1},{32579,1},{98731,2},{104729,3}} ?shorten(mpz_factors(d,1),"factors",2) -- {1,29269,"...","364792324112959639158827476291","10677106534462215678539721403561279"," (48 factors)"}
Note the value in (string) d exceeds the precision limit of an IEEE-754 float, and would trigger a suitable human readable run-time error if passed to any of the non-mpz routines. Sadly, 1200034005600070000008900000000000000000 exceeds the capabilities of my mpz_pollard_rho(), which I had hoped to showcase - perhaps you would like to improve it?
Phixmonti
/# Rosetta Code problem: http://rosettacode.org/wiki/Factors_of_an_integer
by Galileo, 05/2022 #/
include ..\Utilitys.pmt
def Factors >ps
( ( 1 tps 2 / ) for tps over mod if drop endif endfor ps> )
enddef
11 Factors
21 Factors
32 factors
45 factors
67 factors
96 factors
pstack- Output:
[[1, 11], [1, 3, 7, 21], [1, 2, 4, 8, 16, 32], [1, 3, 5, 9, 15, 45], [1, 67], [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96]] === Press any key to exit ===
PHP
function GetFactors($n){
$factors = array(1, $n);
for($i = 2; $i * $i <= $n; $i++){
if($n % $i == 0){
$factors[] = $i;
if($i * $i != $n)
$factors[] = $n/$i;
}
}
sort($factors);
return $factors;
}Picat
List comprehension
factors(N) = [[D,N // D] : D in 1..N.sqrt.floor, N mod D == 0].flatten.sort_remove_dups.Recursion
factors2(N,Fs) :-
integer(N),
N > 0,
Fs = findall(F,factors2_(N,F)).sort_remove_dups.
factors2_(N,F) :-
L = floor(sqrt(N)),
between(1,L,X),
0 == N mod X,
( F = X ; F = N // X ).Loop using set
factors3(N) = Set.keys.sort =>
Set = new_set(),
Set.put(1),
Set.put(N),
foreach(I in 1..floor(sqrt(N)), N mod I == 0)
Set.put(I),
Set.put(N//I)
end.Comparison
Let's compare with 18! (6402373705728000) which has 14688 factors. The recursive version is slightly faster than the loop + set version.
go =>
N = 6402373705728000, % factorial(18),
println("factors:"),
time(_Fs1 = factors(N)) ,
println("factors2:"),
time(factors2(N,_Fs2)),
println("factors3:"),
time(Fs3=factors3(N)).len),- Output:
factors: CPU time 3.938 seconds. factors2: CPU time 3.108 seconds. factors3: CPU time 3.159 seconds.
PicoLisp
(de factors (N)
(filter
'((D) (=0 (% N D)))
(range 1 N) ) )PILOT
T :Enter a number.
A :#n
C :factor = 1
T :The factors of #n are:
*Loop
C :remainder = n % factor
T ( remainder = 0 ) :#factor
J ( factor = n ) :*Finished
C :factor = factor + 1
J :*Loop
*Finished
END:PL/0
PL/0 does not handle strings. So, no prompt. The program waits for entering a number, and then displays the factors.
var n, absn, ndiv2, i;
begin
? n;
absn := n;
if n < 0 then absn := -n;
ndiv2 := absn / 2;
i := 1;
while i <= ndiv2 do
begin
if (absn / i) * i = absn then ! i;
i := i + 1
end;
! absn;
end.4 runs.
- Input:
1
- Output:
1
- Input:
11
- Output:
1
2
3
4
6
12
- Input:
13
- Output:
1
13
- Input:
-22222
- Output:
1
2
41
82
271
542
11111
22222
PL/I
factors: procedure options(main);
declare i binary( 15 )fixed;
declare n binary( 15 )fixed;
do n = 90 to 100;
put skip list( 'factors of: ', n, ': ' );
do i = 1 to n;
if mod(n, i) = 0 then put edit( i )(f(4));
end;
end;
end factors;- Output:
factors of: 90 : 1 2 3 5 6 9 10 15 18 30 45 90 factors of: 91 : 1 7 13 91 factors of: 92 : 1 2 4 23 46 92 factors of: 93 : 1 3 31 93 factors of: 94 : 1 2 47 94 factors of: 95 : 1 5 19 95 factors of: 96 : 1 2 3 4 6 8 12 16 24 32 48 96 factors of: 97 : 1 97 factors of: 98 : 1 2 7 14 49 98 factors of: 99 : 1 3 9 11 33 99 factors of: 100 : 1 2 4 5 10 20 25 50 100
See also #Polyglot:PL/I and PL/M
PL/M
Plain English
To run:
Start up.
Show the factors of 11.
Show the factors of 21.
Show the factors of 519.
Wait for the escape key.
Shut down.
To show the factors of a number:
Write "The factors of " then the number then ":" on the console.
Find a square root of the number.
Loop.
If a counter is past the square root, write "" on the console; exit.
Divide the number by the counter giving a quotient and a remainder.
If the remainder is 0, show the counter and the quotient.
Repeat.
A factor is a number.
To show a factor and another factor:
If the factor is not the other factor, write "" then the factor then " " then the other factor then " " on the console without advancing; exit.
Write "" then the factor on the console without advancing.- Output:
The factors of 11: 1 11 The factors of 21: 1 21 3 7 The factors of 519: 1 519 3 173
Polyglot:PL/I and PL/M
... under CP/M (or an emulator)
Should work with many PL/I implementations.
The PL/I include file "pg.inc" can be found on the Polyglot:PL/I and PL/M page.
Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler.
factors_100H: procedure options (main);
/* PL/I DEFINITIONS */
%include 'pg.inc';
/* PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. */ /*
DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE';
DECLARE SADDR LITERALLY '.', BIT LITERALLY 'BYTE';
DECLARE FIXED LITERALLY ' ';
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PRSTRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PRCHAR: PROCEDURE( C ); DECLARE C CHARACTER; CALL BDOS( 2, C ); END;
PRNL: PROCEDURE; CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END;
PRNUMBER: PROCEDURE( N );
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
N$STR( W := LAST( N$STR ) ) = '$';
N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL BDOS( 9, .N$STR( W ) );
END PRNUMBER;
MODF: PROCEDURE( A, B )ADDRESS;
DECLARE ( A, B )ADDRESS;
RETURN( A MOD B );
END MODF;
/* END LANGUAGE DEFINITIONS */
/* TASK */
DECLARE ( I, N ) FIXED BINARY;
DO N = 90 TO 100;
CALL PRSTRING( SADDR( 'FACTORS OF: $' ) );
CALL PRNUMBER( N );
CALL PRCHAR( ':' );
DO I = 1 TO N;
IF MODF( N, I ) = 0 THEN DO;
CALL PRCHAR( ' ' );
CALL PRNUMBER( I );
END;
END;
CALL PRNL;
END;
EOF: end factors_100H;- Output:
FACTORS OF: 90: 1 2 3 5 6 9 10 15 18 30 45 90 FACTORS OF: 91: 1 7 13 91 FACTORS OF: 92: 1 2 4 23 46 92 FACTORS OF: 93: 1 3 31 93 FACTORS OF: 94: 1 2 47 94 FACTORS OF: 95: 1 5 19 95 FACTORS OF: 96: 1 2 3 4 6 8 12 16 24 32 48 96 FACTORS OF: 97: 1 97 FACTORS OF: 98: 1 2 7 14 49 98 FACTORS OF: 99: 1 3 9 11 33 99 FACTORS OF: 100: 1 2 4 5 10 20 25 50 100
PowerShell
Straightforward but slow
function Get-Factor ($a) {
1..$a | Where-Object { $a % $_ -eq 0 }
}This one uses a range of integers up to the target number and just filters it using the Where-Object cmdlet. It's very slow though, so it is not very usable for larger numbers.
A little more clever
function Get-Factor ($a) {
1..[Math]::Sqrt($a) `
| Where-Object { $a % $_ -eq 0 } `
| ForEach-Object { $_; $a / $_ } `
| Sort-Object -Unique
}Here the range of integers is only taken up to the square root of the number, the same filtering applies. Afterwards the corresponding larger factors are calculated and sent down the pipeline along with the small ones found earlier.
ProDOS
Uses the math module:
editvar /newvar /value=a /userinput=1 /title=Enter an integer:
do /delimspaces %% -a- >b
printline Factors of -a-: -b-Prolog
Simple Brute Force Implementation
brute_force_factors( N , Fs ) :-
integer(N) ,
N > 0 ,
setof( F , ( between(1,N,F) , N mod F =:= 0 ) , Fs )
.A Slightly Smarter Implementation
smart_factors(N,Fs) :-
integer(N) ,
N > 0 ,
setof( F , factor(N,F) , Fs )
.
factor(N,F) :-
L is floor(sqrt(N)) ,
between(1,L,X) ,
0 =:= N mod X ,
( F = X ; F is N // X )
.Not every Prolog has between/3: you might need this:
between(X,Y,Z) :-
integer(X) ,
integer(Y) ,
X =< Z ,
between1(X,Y,Z)
.
between1(X,Y,X) :-
X =< Y
.
between1(X,Y,Z) :-
X < Y ,
X1 is X+1 ,
between1(X1,Y,Z)
.- Output:
?- N=36 ,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ). N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] ; N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] . ?- N=53,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ). N = 53, Factors = [1, 53] ; N = 53, Factors = [1, 53] . ?- N=100,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] ; N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] . ?- N=144,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] ; N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] . ?- N=32765,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32765, Factors = [1, 5, 6553, 32765] ; N = 32765, Factors = [1, 5, 6553, 32765] . ?- N=32766,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] ; N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] . 38 ?- N=32767,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] ; N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] .
Python
Naive and slow but simplest (check all numbers from 1 to n):
>>> def factors(n):
return [i for i in range(1, n + 1) if not n%i]Slightly better (realize that there are no factors between n/2 and n):
>>> def factors(n):
return [i for i in range(1, n//2 + 1) if not n%i] + [n]
>>> factors(45)
[1, 3, 5, 9, 15, 45]Much better (realize that factors come in pairs, the smaller of which is no bigger than sqrt(n)):
from math import isqrt
def factor(n):
factors1, factors2 = [], []
for x in range(1, isqrt(n)):
if n % x == 0:
factors1.append(x)
factors2.append(n // x)
x += 1
if x * x == n:
factors1.append(x)
factors1.extend(reversed(factors2))
return factors1
for i in 45, 53, 64:
print("%i: factors: %s" % (i, factor(i)))45: factors: [1, 3, 5, 9, 15, 45] 53: factors: [1, 53] 64: factors: [1, 2, 4, 8, 16, 32, 64]
More efficient when factoring many numbers:
from itertools import chain, cycle, accumulate # last of which is Python 3 only
def factors(n):
def prime_powers(n):
# c goes through 2, 3, 5, then the infinite (6n+1, 6n+5) series
for c in accumulate(chain([2, 1, 2], cycle([2,4]))):
if c*c > n: break
if n%c: continue
d,p = (), c
while not n%c:
n,p,d = n//c, p*c, d + (p,)
yield(d)
if n > 1: yield((n,))
r = [1]
for e in prime_powers(n):
r += [a*b for a in r for b in e]
return rQuackery
sqrt+ is defined at Isqrt (integer square root) of X#Quackery. It returns the integer square root and remainder (i.e. the square root of 11 is 3 remainder 2, because three squared plus two equals eleven.) If the number is a perfect square the remainder is zero. This is used to remove a duplicate factor from the list of factors which is generated when finding the factors of a perfect square.
The nest editing at the end of the definition (i.e. the code after the drop on a line by itself) removes a duplicate factor if there is one, and arranges the factors in ascending numerical order at the same time.
[ [] swap
dup sqrt+ 0 = dip
[ times
[ dup i^ 1+ /mod iff
drop done
rot join
i^ 1+ join swap ]
drop
dup size 2 / split ]
if [ -1 split drop ]
swap join ] is factors ( n --> [ )
20 times
[ i^ 1+ dup
dup 10 < if sp
echo
say ": "
factors witheach
[ echo i if say ", " ]
cr ]- Output:
1: 1 2: 1, 2 3: 1, 3 4: 1, 2, 4 5: 1, 5 6: 1, 2, 3, 6 7: 1, 7 8: 1, 2, 4, 8 9: 1, 3, 9 10: 1, 2, 5, 10 11: 1, 11 12: 1, 2, 3, 4, 6, 12 13: 1, 13 14: 1, 2, 7, 14 15: 1, 3, 5, 15 16: 1, 2, 4, 8, 16 17: 1, 17 18: 1, 2, 3, 6, 9, 18 19: 1, 19 20: 1, 2, 4, 5, 10, 20
R
Array solution
factors <- function(n)
{
if(length(n) > 1)
{
lapply(as.list(n), factors)
} else
{
one.to.n <- seq_len(n)
one.to.n[(n %% one.to.n) == 0]
}
}- Output:
>factors(60) [1] 1 2 3 4 5 6 10 12 15 20 30 60 >factors(c(45, 53, 64)) [[1]] [1] 1 3 5 9 15 45 [[2]] [1] 1 53 [[3]] [1] 1 2 4 8 16 32 64
Filter solution
With identical output, a more idiomatic way is to use R's Filter.
factors <- function(n) c(Filter(function(x) n %% x == 0, seq_len(n %/% 2)), n)
#Vectorize is an interesting alternative to the previous solution's lapply.
manyFactors <- function(vec) Vectorize(factors)(vec)Racket
#lang racket
;; a naive version
(define (naive-factors n)
(for/list ([i (in-range 1 (add1 n))] #:when (zero? (modulo n i))) i))
(naive-factors 120) ; -> '(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120)
;; much better: use `factorize' to get prime factors and construct the
;; list of results from that
(require math)
(define (factors n)
(sort (for/fold ([l '(1)]) ([p (factorize n)])
(append (for*/list ([e (in-range 1 (add1 (cadr p)))] [x l])
(* x (expt (car p) e)))
l))
<))
(naive-factors 120) ; -> same
;; to see how fast it is:
(define huge 1200034005600070000008900000000000000000)
(time (length (factors huge)))
;; I get 42ms for getting a list of 7776 numbers
;; but actually the math library comes with a `divisors' function that
;; does the same, except even faster
(divisors 120) ; -> same
(time (length (divisors huge)))
;; And this one clocks at 17msRaku
(formerly Perl 6)
Brute-force
Naive, brute-force, and slow, but ok for small numbers.
sub factors (Int $n) { (1..$n).grep($n %% *) }Optimized
If you don't want to roll your own.
use Prime::Factor;
put divisors :s, 2⁹⁹ + 1;
say (now - INIT now).round(.001) ~' seconds';- Output:
1 3 9 19 27 57 67 171 201 513 603 683 1273 1809 2049 3819 5347 6147 11457 12977 16041 18441 20857 34371 38931 45761 48123 62571 101593 116793 137283 144369 187713 304779 350379 358249 396283 411849 563139 869459 914337 1074747 1188849 1235547 1397419 2608377 2743011 3224241 3566547 3652001 4192257 6806731 7825131 9672723 10699641 10956003 12576771 14245331 20420193 23475393 26550961 32868009 37730313 42735993 61260579 69388019 79652883 98604027 111522379 128207979 183781737 208164057 238958649 244684067 270661289 334567137 384623937 624492171 716875947 734052201 811983867 954437177 1003701411 1873476513 2118925201 2202156603 2435951601 2863311531 3011104233 4648997273 6356775603 6606469809 7307854803 7471999393 8589934593 13946991819 18134306363 19070326809 22415998179 25769803779 41840975457 54402919089 57210980427 67247994537 76169784857 125522926371 141967988467 163208757267 201743983611 228509354571 425903965401 489626271801 685528063713 1277711896203 1447225912283 2056584191139 3833135688609 4341677736849 5103375585419 13025033210547 15310126756257 39075099631641 45930380268771 96964136122961 137791140806313 242099935645987 290892408368883 726299806937961 872677225106649 2178899420813883 2618031675319947 4599898777273753 6536698262441649 13799696331821259 16220695688281129 41399088995463777 48662087064843387 124197266986391331 145986261194530161 165354256046209121 308193218077341451 437958783583590483 496062768138627363 924579654232024353 1294508355899092489 1488188304415882089 2773738962696073059 3141730864877973299 3883525067697277467 4464564913247646267 5049478357768350859 8321216888088219177 9425192594633919897 11078735155096011107 11650575203091832401 15148435073305052577 24595658762082757291 28275577783901759691 33236205465288033321 34951725609275497203 45445305219915157731 73786976286248271873 84826733351705279073 86732059845239196763 95940088797598666321 99708616395864099963 136335915659745473193 210495967946824211033 221360928858744815619 260196179535717590289 287820266392795998963 299125849187592299889 338315049970479507553 631487903840472633099 664082786576234446857 780588538607152770867 863460799178387996889 884149207079080169987 1014945149911438522659 1647909137059544738497 1894463711521417899297 2341765615821458312601 2590382397535163990667 2652447621237240509961 3044835449734315567977 3448793718355783636697 4943727411178634215491 5683391134564253697891 6427985949439110643507 7957342863711721529883 9134506349202946703931 10346381155067350910091 14831182233535902646473 16798834934502523229753 19283957848317331930521 23872028591135164589649 26999560778987372043073 31039143465202052730273 44493546700607707939419 50396504803507569689259 57851873544951995791563 59237996874298371389129 65527080648759889097243 80998682336962116129219 93117430395606158190819 151189514410522709067777 173555620634855987374689 177713990622895114167387 196581241946279667291729 231069179129837503658699 242996047010886348387657 453568543231568127203331 512991654800760068818387 533141971868685342502161 589743725838839001875187 693207537389512510976097 728988141032659045162971 1125521940611669056393451 1538974964402280206455161 1599425915606056027506483 1769231177516517005625561 1808970572192153926885891 2079622612168537532928291 3376565821835007169180353 4390314403466912569515281 4616924893206840619365483 5426911716576461780657673 6238867836505612598784873 10129697465505021507541059 13170943210400737708545843 13850774679620521858096449 16280735149729385341973019 18440700012048375105418859 30389092396515064522623177 34370440871650924610831929 39512829631202213125637529 48842205449188156025919057 55322100036145125316256577 103111322614952773832495787 118538488893606639376912587 165966300108435375948769731 309333967844858321497487361 350373300228919127002958321 497898900325306127846309193 928001903534574964492462083 1051119900686757381008874963 1235526900807241132063063553 3153359702060272143026624889 3706580702421723396189190659 9460079106180816429079874667 11119742107265170188567571977 23475011115337581509198207507 33359226321795510565702715931 70425033346012744527594622521 211275100038038233582783867563 633825300114114700748351602689 0.046 seconds
Red
Red []
factors: function [n [integer!]] [
n: absolute n
collect [
repeat i (sq: sqrt n) - 1 [
if n % i = 0 [
keep i
keep n / i
]
]
if sq = sq: to-integer sq [keep sq]
]
]
foreach num [
24
-64 ; negative
64 ; square
101 ; prime
123456789 ; large
][
print mold/flat sort factors num
]Refal
$ENTRY Go {
= <Prout <Factors 120>>;
}
Factors {
s.N = <Factors (s.N 1)>;
(s.N s.D), <Compare s.N <* s.D s.D>>: '-' = ;
(s.N s.D), <Divmod s.N s.D>: {
(s.D) 0 = s.D;
(s.F) 0 = s.D <Factors (s.N <+ 1 s.D>)> s.F;
(s.X) s.Y = <Factors (s.N <+ 1 s.D>)>;
};
};- Output:
1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
Relation
program factors(num)
relation fact
insert 1
set i = 2
while i < num / 2
if num / i = floor(num/i)
insert i
end if
set i = i + 1
end while
insert num
print
end programREXX
optimized version
This REXX version has no effective limits on the number of decimal digits in the number to be factored [by adjusting the number of digits (precision)].
This REXX version also supports negative integers and zero.
It also indicates primes in the output listing as well as the number of divisors.
It also displays a final count of the number of primes found.
This REXX version is about 22% faster than the alternate REXX version (2nd version).
/*REXX program displays divisors of any [negative/zero/positive] integer or a range.*/
parse arg LO HI inc . /*obtain the optional args*/
HI= word(HI LO 20, 1); LO= word(LO 1,1); inc= word(inc 1,1) /*define the range options*/
w= length(HI) + 2; numeric digits max(9, w-2); != '∞' /*decimal digits for // */
@.=left('',7); @.1= "{unity}"; @.2= '[prime]'; @.!= " {∞} " /*define some literals. */
say center('n', w) "#divisors" center('divisors', 60) /*display the header. */
say copies('═', w) "═════════" copies('═' , 60) /* " " separator. */
pn= 0 /*count of prime numbers. */
do k=2 until sq.k>=HI; sq.k= k*k /*memoization for squares.*/
end /*k*/
do n=LO to HI by inc; $= divs(n); #= words($) /*get list of divs; # divs*/
if $==! then do; #= !; $= ' (infinite)'; end /*handle case for infinity*/
p= @.#; if n<0 then if n\==-1 then p= @.. /* " " " negative*/
if p==@.2 then pn= pn + 1 /*Prime? Then bump counter*/
say center(n, w) center('['#"]", 9) "──► " p ' ' $
end /*n*/ /* [↑] process a range of integers. */
say
say right(pn, 20) ' primes were found.' /*display the number of primes found. */
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
divs: procedure expose sq.; parse arg x 1 b; a=1 /*set X and B to the 1st argument. */
if x<2 then do; x= abs(x); if x==1 then return 1; if x==0 then return '∞'; b=x
end
odd= x // 2 /* [↓] process EVEN or ODD ints. ___*/
do j=2+odd by 1+odd while sq.j<x /*divide by all the integers up to √ x */
if x//j==0 then do; a=a j; b=x%j b; end /*÷? Add divisors to α and ß lists*/
end /*j*/ /* [↑] % ≡ integer division. ___*/
if sq.j==x then return a j b /*Was X a square? Then insert √ x */
return a b /*return the divisors of both lists. */- output when using the input of: -6 200
(Shown at 3/4 size.)
n #divisors divisors
══════ ═════════ ════════════════════════════════════════════════════════════
-6 [4] ──► 1 2 3 6
-5 [2] ──► 1 5
-4 [3] ──► 1 2 4
-3 [2] ──► 1 3
-2 [2] ──► 1 2
-1 [1] ──► {unity} 1
0 [∞] ──► {∞} (infinite)
1 [1] ──► {unity} 1
2 [2] ──► [prime] 1 2
3 [2] ──► [prime] 1 3
4 [3] ──► 1 2 4
5 [2] ──► [prime] 1 5
6 [4] ──► 1 2 3 6
7 [2] ──► [prime] 1 7
8 [4] ──► 1 2 4 8
9 [3] ──► 1 3 9
10 [4] ──► 1 2 5 10
11 [2] ──► [prime] 1 11
12 [6] ──► 1 2 3 4 6 12
13 [2] ──► [prime] 1 13
14 [4] ──► 1 2 7 14
15 [4] ──► 1 3 5 15
16 [5] ──► 1 2 4 8 16
17 [2] ──► [prime] 1 17
18 [6] ──► 1 2 3 6 9 18
19 [2] ──► [prime] 1 19
20 [6] ──► 1 2 4 5 10 20
21 [4] ──► 1 3 7 21
22 [4] ──► 1 2 11 22
23 [2] ──► [prime] 1 23
24 [8] ──► 1 2 3 4 6 8 12 24
25 [3] ──► 1 5 25
26 [4] ──► 1 2 13 26
27 [4] ──► 1 3 9 27
28 [6] ──► 1 2 4 7 14 28
29 [2] ──► [prime] 1 29
30 [8] ──► 1 2 3 5 6 10 15 30
31 [2] ──► [prime] 1 31
32 [6] ──► 1 2 4 8 16 32
33 [4] ──► 1 3 11 33
34 [4] ──► 1 2 17 34
35 [4] ──► 1 5 7 35
36 [9] ──► 1 2 3 4 6 9 12 18 36
37 [2] ──► [prime] 1 37
38 [4] ──► 1 2 19 38
39 [4] ──► 1 3 13 39
40 [8] ──► 1 2 4 5 8 10 20 40
41 [2] ──► [prime] 1 41
42 [8] ──► 1 2 3 6 7 14 21 42
43 [2] ──► [prime] 1 43
44 [6] ──► 1 2 4 11 22 44
45 [6] ──► 1 3 5 9 15 45
46 [4] ──► 1 2 23 46
47 [2] ──► [prime] 1 47
48 [10] ──► 1 2 3 4 6 8 12 16 24 48
49 [3] ──► 1 7 49
50 [6] ──► 1 2 5 10 25 50
51 [4] ──► 1 3 17 51
52 [6] ──► 1 2 4 13 26 52
53 [2] ──► [prime] 1 53
54 [8] ──► 1 2 3 6 9 18 27 54
55 [4] ──► 1 5 11 55
56 [8] ──► 1 2 4 7 8 14 28 56
57 [4] ──► 1 3 19 57
58 [4] ──► 1 2 29 58
59 [2] ──► [prime] 1 59
60 [12] ──► 1 2 3 4 5 6 10 12 15 20 30 60
61 [2] ──► [prime] 1 61
62 [4] ──► 1 2 31 62
63 [6] ──► 1 3 7 9 21 63
64 [7] ──► 1 2 4 8 16 32 64
65 [4] ──► 1 5 13 65
66 [8] ──► 1 2 3 6 11 22 33 66
67 [2] ──► [prime] 1 67
68 [6] ──► 1 2 4 17 34 68
69 [4] ──► 1 3 23 69
70 [8] ──► 1 2 5 7 10 14 35 70
71 [2] ──► [prime] 1 71
72 [12] ──► 1 2 3 4 6 8 9 12 18 24 36 72
73 [2] ──► [prime] 1 73
74 [4] ──► 1 2 37 74
75 [6] ──► 1 3 5 15 25 75
76 [6] ──► 1 2 4 19 38 76
77 [4] ──► 1 7 11 77
78 [8] ──► 1 2 3 6 13 26 39 78
79 [2] ──► [prime] 1 79
80 [10] ──► 1 2 4 5 8 10 16 20 40 80
81 [5] ──► 1 3 9 27 81
82 [4] ──► 1 2 41 82
83 [2] ──► [prime] 1 83
84 [12] ──► 1 2 3 4 6 7 12 14 21 28 42 84
85 [4] ──► 1 5 17 85
86 [4] ──► 1 2 43 86
87 [4] ──► 1 3 29 87
88 [8] ──► 1 2 4 8 11 22 44 88
89 [2] ──► [prime] 1 89
90 [12] ──► 1 2 3 5 6 9 10 15 18 30 45 90
91 [4] ──► 1 7 13 91
92 [6] ──► 1 2 4 23 46 92
93 [4] ──► 1 3 31 93
94 [4] ──► 1 2 47 94
95 [4] ──► 1 5 19 95
96 [12] ──► 1 2 3 4 6 8 12 16 24 32 48 96
97 [2] ──► [prime] 1 97
98 [6] ──► 1 2 7 14 49 98
99 [6] ──► 1 3 9 11 33 99
100 [9] ──► 1 2 4 5 10 20 25 50 100
101 [2] ──► [prime] 1 101
102 [8] ──► 1 2 3 6 17 34 51 102
103 [2] ──► [prime] 1 103
104 [8] ──► 1 2 4 8 13 26 52 104
105 [8] ──► 1 3 5 7 15 21 35 105
106 [4] ──► 1 2 53 106
107 [2] ──► [prime] 1 107
108 [12] ──► 1 2 3 4 6 9 12 18 27 36 54 108
109 [2] ──► [prime] 1 109
110 [8] ──► 1 2 5 10 11 22 55 110
111 [4] ──► 1 3 37 111
112 [10] ──► 1 2 4 7 8 14 16 28 56 112
113 [2] ──► [prime] 1 113
114 [8] ──► 1 2 3 6 19 38 57 114
115 [4] ──► 1 5 23 115
116 [6] ──► 1 2 4 29 58 116
117 [6] ──► 1 3 9 13 39 117
118 [4] ──► 1 2 59 118
119 [4] ──► 1 7 17 119
120 [16] ──► 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
121 [3] ──► 1 11 121
122 [4] ──► 1 2 61 122
123 [4] ──► 1 3 41 123
124 [6] ──► 1 2 4 31 62 124
125 [4] ──► 1 5 25 125
126 [12] ──► 1 2 3 6 7 9 14 18 21 42 63 126
127 [2] ──► [prime] 1 127
128 [8] ──► 1 2 4 8 16 32 64 128
129 [4] ──► 1 3 43 129
130 [8] ──► 1 2 5 10 13 26 65 130
131 [2] ──► [prime] 1 131
132 [12] ──► 1 2 3 4 6 11 12 22 33 44 66 132
133 [4] ──► 1 7 19 133
134 [4] ──► 1 2 67 134
135 [8] ──► 1 3 5 9 15 27 45 135
136 [8] ──► 1 2 4 8 17 34 68 136
137 [2] ──► [prime] 1 137
138 [8] ──► 1 2 3 6 23 46 69 138
139 [2] ──► [prime] 1 139
140 [12] ──► 1 2 4 5 7 10 14 20 28 35 70 140
141 [4] ──► 1 3 47 141
142 [4] ──► 1 2 71 142
143 [4] ──► 1 11 13 143
144 [15] ──► 1 2 3 4 6 8 9 12 16 18 24 36 48 72 144
145 [4] ──► 1 5 29 145
146 [4] ──► 1 2 73 146
147 [6] ──► 1 3 7 21 49 147
148 [6] ──► 1 2 4 37 74 148
149 [2] ──► [prime] 1 149
150 [12] ──► 1 2 3 5 6 10 15 25 30 50 75 150
151 [2] ──► [prime] 1 151
152 [8] ──► 1 2 4 8 19 38 76 152
153 [6] ──► 1 3 9 17 51 153
154 [8] ──► 1 2 7 11 14 22 77 154
155 [4] ──► 1 5 31 155
156 [12] ──► 1 2 3 4 6 12 13 26 39 52 78 156
157 [2] ──► [prime] 1 157
158 [4] ──► 1 2 79 158
159 [4] ──► 1 3 53 159
160 [12] ──► 1 2 4 5 8 10 16 20 32 40 80 160
161 [4] ──► 1 7 23 161
162 [10] ──► 1 2 3 6 9 18 27 54 81 162
163 [2] ──► [prime] 1 163
164 [6] ──► 1 2 4 41 82 164
165 [8] ──► 1 3 5 11 15 33 55 165
166 [4] ──► 1 2 83 166
167 [2] ──► [prime] 1 167
168 [16] ──► 1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168
169 [3] ──► 1 13 169
170 [8] ──► 1 2 5 10 17 34 85 170
171 [6] ──► 1 3 9 19 57 171
172 [6] ──► 1 2 4 43 86 172
173 [2] ──► [prime] 1 173
174 [8] ──► 1 2 3 6 29 58 87 174
175 [6] ──► 1 5 7 25 35 175
176 [10] ──► 1 2 4 8 11 16 22 44 88 176
177 [4] ──► 1 3 59 177
178 [4] ──► 1 2 89 178
179 [2] ──► [prime] 1 179
180 [18] ──► 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180
181 [2] ──► [prime] 1 181
182 [8] ──► 1 2 7 13 14 26 91 182
183 [4] ──► 1 3 61 183
184 [8] ──► 1 2 4 8 23 46 92 184
185 [4] ──► 1 5 37 185
186 [8] ──► 1 2 3 6 31 62 93 186
187 [4] ──► 1 11 17 187
188 [6] ──► 1 2 4 47 94 188
189 [8] ──► 1 3 7 9 21 27 63 189
190 [8] ──► 1 2 5 10 19 38 95 190
191 [2] ──► [prime] 1 191
192 [14] ──► 1 2 3 4 6 8 12 16 24 32 48 64 96 192
193 [2] ──► [prime] 1 193
194 [4] ──► 1 2 97 194
195 [8] ──► 1 3 5 13 15 39 65 195
196 [9] ──► 1 2 4 7 14 28 49 98 196
197 [2] ──► [prime] 1 197
198 [12] ──► 1 2 3 6 9 11 18 22 33 66 99 198
199 [2] ──► [prime] 1 199
200 [12] ──► 1 2 4 5 8 10 20 25 40 50 100 200
46 primes were found.
Alternate Version
/* REXX ***************************************************************
* Program to calculate and show divisors of positive integer(s).
* 03.08.2012 Walter Pachl simplified the above somewhat
* in particular I see no benefit from divAdd procedure
* 04.08.2012 the reference to 'above' is no longer valid since that
* was meanwhile changed for the better.
* 04.08.2012 took over some improvements from new above
**********************************************************************/
Parse arg low high .
Select
When low='' Then Parse Value '1 200' with low high
When high='' Then high=low
Otherwise Nop
End
do j=low to high
say ' n = ' right(j,6) " divisors = " divs(j)
end
exit
divs: procedure; parse arg x
if x==1 then return 1 /*handle special case of 1 */
Parse Value '1' x With lo hi /*initialize lists: lo=1 hi=x */
odd=x//2 /* 1 if x is odd */
Do j=2+odd By 1+odd While j*j<x /*divide by numbers<sqrt(x) */
if x//j==0 then Do /*Divisible? Add two divisors:*/
lo=lo j /* list low divisors */
hi=x%j hi /* list high divisors */
End
End
If j*j=x Then /*for a square number as input */
lo=lo j /* add its square root */
return lo hi /* return both lists */- output when using the default input:
(Shown at 3/4 size.)
n = 1 divisors = 1 n = 2 divisors = 1 2 n = 3 divisors = 1 3 n = 4 divisors = 1 2 4 n = 5 divisors = 1 5 n = 6 divisors = 1 2 3 6 n = 7 divisors = 1 7 n = 8 divisors = 1 2 4 8 n = 9 divisors = 1 3 9 n = 10 divisors = 1 2 5 10 n = 11 divisors = 1 11 n = 12 divisors = 1 2 3 4 6 12 n = 13 divisors = 1 13 n = 14 divisors = 1 2 7 14 n = 15 divisors = 1 3 5 15 n = 16 divisors = 1 2 4 8 16 n = 17 divisors = 1 17 n = 18 divisors = 1 2 3 6 9 18 n = 19 divisors = 1 19 n = 20 divisors = 1 2 4 5 10 20 n = 21 divisors = 1 3 7 21 n = 22 divisors = 1 2 11 22 n = 23 divisors = 1 23 n = 24 divisors = 1 2 3 4 6 8 12 24 n = 25 divisors = 1 5 25 n = 26 divisors = 1 2 13 26 n = 27 divisors = 1 3 9 27 n = 28 divisors = 1 2 4 7 14 28 n = 29 divisors = 1 29 n = 30 divisors = 1 2 3 5 6 10 15 30 n = 31 divisors = 1 31 n = 32 divisors = 1 2 4 8 16 32 n = 33 divisors = 1 3 11 33 n = 34 divisors = 1 2 17 34 n = 35 divisors = 1 5 7 35 n = 36 divisors = 1 2 3 4 6 9 12 18 36 n = 37 divisors = 1 37 n = 38 divisors = 1 2 19 38 n = 39 divisors = 1 3 13 39 n = 40 divisors = 1 2 4 5 8 10 20 40 n = 41 divisors = 1 41 n = 42 divisors = 1 2 3 6 7 14 21 42 n = 43 divisors = 1 43 n = 44 divisors = 1 2 4 11 22 44 n = 45 divisors = 1 3 5 9 15 45 n = 46 divisors = 1 2 23 46 n = 47 divisors = 1 47 n = 48 divisors = 1 2 3 4 6 8 12 16 24 48 n = 49 divisors = 1 7 49 n = 50 divisors = 1 2 5 10 25 50 n = 51 divisors = 1 3 17 51 n = 52 divisors = 1 2 4 13 26 52 n = 53 divisors = 1 53 n = 54 divisors = 1 2 3 6 9 18 27 54 n = 55 divisors = 1 5 11 55 n = 56 divisors = 1 2 4 7 8 14 28 56 n = 57 divisors = 1 3 19 57 n = 58 divisors = 1 2 29 58 n = 59 divisors = 1 59 n = 60 divisors = 1 2 3 4 5 6 10 12 15 20 30 60 n = 61 divisors = 1 61 n = 62 divisors = 1 2 31 62 n = 63 divisors = 1 3 7 9 21 63 n = 64 divisors = 1 2 4 8 16 32 64 n = 65 divisors = 1 5 13 65 n = 66 divisors = 1 2 3 6 11 22 33 66 n = 67 divisors = 1 67 n = 68 divisors = 1 2 4 17 34 68 n = 69 divisors = 1 3 23 69 n = 70 divisors = 1 2 5 7 10 14 35 70 n = 71 divisors = 1 71 n = 72 divisors = 1 2 3 4 6 8 9 12 18 24 36 72 n = 73 divisors = 1 73 n = 74 divisors = 1 2 37 74 n = 75 divisors = 1 3 5 15 25 75 n = 76 divisors = 1 2 4 19 38 76 n = 77 divisors = 1 7 11 77 n = 78 divisors = 1 2 3 6 13 26 39 78 n = 79 divisors = 1 79 n = 80 divisors = 1 2 4 5 8 10 16 20 40 80 n = 81 divisors = 1 3 9 27 81 n = 82 divisors = 1 2 41 82 n = 83 divisors = 1 83 n = 84 divisors = 1 2 3 4 6 7 12 14 21 28 42 84 n = 85 divisors = 1 5 17 85 n = 86 divisors = 1 2 43 86 n = 87 divisors = 1 3 29 87 n = 88 divisors = 1 2 4 8 11 22 44 88 n = 89 divisors = 1 89 n = 90 divisors = 1 2 3 5 6 9 10 15 18 30 45 90 n = 91 divisors = 1 7 13 91 n = 92 divisors = 1 2 4 23 46 92 n = 93 divisors = 1 3 31 93 n = 94 divisors = 1 2 47 94 n = 95 divisors = 1 5 19 95 n = 96 divisors = 1 2 3 4 6 8 12 16 24 32 48 96 n = 97 divisors = 1 97 n = 98 divisors = 1 2 7 14 49 98 n = 99 divisors = 1 3 9 11 33 99 n = 100 divisors = 1 2 4 5 10 20 25 50 100 n = 101 divisors = 1 101 n = 102 divisors = 1 2 3 6 17 34 51 102 n = 103 divisors = 1 103 n = 104 divisors = 1 2 4 8 13 26 52 104 n = 105 divisors = 1 3 5 7 15 21 35 105 n = 106 divisors = 1 2 53 106 n = 107 divisors = 1 107 n = 108 divisors = 1 2 3 4 6 9 12 18 27 36 54 108 n = 109 divisors = 1 109 n = 110 divisors = 1 2 5 10 11 22 55 110 n = 111 divisors = 1 3 37 111 n = 112 divisors = 1 2 4 7 8 14 16 28 56 112 n = 113 divisors = 1 113 n = 114 divisors = 1 2 3 6 19 38 57 114 n = 115 divisors = 1 5 23 115 n = 116 divisors = 1 2 4 29 58 116 n = 117 divisors = 1 3 9 13 39 117 n = 118 divisors = 1 2 59 118 n = 119 divisors = 1 7 17 119 n = 120 divisors = 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 n = 121 divisors = 1 11 121 n = 122 divisors = 1 2 61 122 n = 123 divisors = 1 3 41 123 n = 124 divisors = 1 2 4 31 62 124 n = 125 divisors = 1 5 25 125 n = 126 divisors = 1 2 3 6 7 9 14 18 21 42 63 126 n = 127 divisors = 1 127 n = 128 divisors = 1 2 4 8 16 32 64 128 n = 129 divisors = 1 3 43 129 n = 130 divisors = 1 2 5 10 13 26 65 130 n = 131 divisors = 1 131 n = 132 divisors = 1 2 3 4 6 11 12 22 33 44 66 132 n = 133 divisors = 1 7 19 133 n = 134 divisors = 1 2 67 134 n = 135 divisors = 1 3 5 9 15 27 45 135 n = 136 divisors = 1 2 4 8 17 34 68 136 n = 137 divisors = 1 137 n = 138 divisors = 1 2 3 6 23 46 69 138 n = 139 divisors = 1 139 n = 140 divisors = 1 2 4 5 7 10 14 20 28 35 70 140 n = 141 divisors = 1 3 47 141 n = 142 divisors = 1 2 71 142 n = 143 divisors = 1 11 13 143 n = 144 divisors = 1 2 3 4 6 8 9 12 16 18 24 36 48 72 144 n = 145 divisors = 1 5 29 145 n = 146 divisors = 1 2 73 146 n = 147 divisors = 1 3 7 21 49 147 n = 148 divisors = 1 2 4 37 74 148 n = 149 divisors = 1 149 n = 150 divisors = 1 2 3 5 6 10 15 25 30 50 75 150 n = 151 divisors = 1 151 n = 152 divisors = 1 2 4 8 19 38 76 152 n = 153 divisors = 1 3 9 17 51 153 n = 154 divisors = 1 2 7 11 14 22 77 154 n = 155 divisors = 1 5 31 155 n = 156 divisors = 1 2 3 4 6 12 13 26 39 52 78 156 n = 157 divisors = 1 157 n = 158 divisors = 1 2 79 158 n = 159 divisors = 1 3 53 159 n = 160 divisors = 1 2 4 5 8 10 16 20 32 40 80 160 n = 161 divisors = 1 7 23 161 n = 162 divisors = 1 2 3 6 9 18 27 54 81 162 n = 163 divisors = 1 163 n = 164 divisors = 1 2 4 41 82 164 n = 165 divisors = 1 3 5 11 15 33 55 165 n = 166 divisors = 1 2 83 166 n = 167 divisors = 1 167 n = 168 divisors = 1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168 n = 169 divisors = 1 13 169 n = 170 divisors = 1 2 5 10 17 34 85 170 n = 171 divisors = 1 3 9 19 57 171 n = 172 divisors = 1 2 4 43 86 172 n = 173 divisors = 1 173 n = 174 divisors = 1 2 3 6 29 58 87 174 n = 175 divisors = 1 5 7 25 35 175 n = 176 divisors = 1 2 4 8 11 16 22 44 88 176 n = 177 divisors = 1 3 59 177 n = 178 divisors = 1 2 89 178 n = 179 divisors = 1 179 n = 180 divisors = 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 n = 181 divisors = 1 181 n = 182 divisors = 1 2 7 13 14 26 91 182 n = 183 divisors = 1 3 61 183 n = 184 divisors = 1 2 4 8 23 46 92 184 n = 185 divisors = 1 5 37 185 n = 186 divisors = 1 2 3 6 31 62 93 186 n = 187 divisors = 1 11 17 187 n = 188 divisors = 1 2 4 47 94 188 n = 189 divisors = 1 3 7 9 21 27 63 189 n = 190 divisors = 1 2 5 10 19 38 95 190 n = 191 divisors = 1 191 n = 192 divisors = 1 2 3 4 6 8 12 16 24 32 48 64 96 192 n = 193 divisors = 1 193 n = 194 divisors = 1 2 97 194 n = 195 divisors = 1 3 5 13 15 39 65 195 n = 196 divisors = 1 2 4 7 14 28 49 98 196 n = 197 divisors = 1 197 n = 198 divisors = 1 2 3 6 9 11 18 22 33 66 99 198 n = 199 divisors = 1 199 n = 200 divisors = 1 2 4 5 8 10 20 25 40 50 100 200
Using REXX libraries
Libraries: How to use
Library: Functions
Library: Numbers
Library: Settings
Library: Abend
Library: Sequences
The procedure Divisors() is also present in Sequences.
include Settings
say version; say 'Factors of an integer'; say
numeric digits 16
parse arg l','h
if l = '' then
l = 1
if h = '' then
h = 100
do i = l to h
f = Divisors(i)
call Charout ,Right(i,3) 'has' Right(f,2) 'divisors: '
do j = 1 to f
call Charout ,divi.divisor.j' '
end
say
end
say Format(Time('e'),,3) 'seconds'; say
exit
Divisors:
/* Divisors of an integer */
procedure expose divi.
arg x
/* Init */
divi. = 0
/* Fast values */
if x = 1 then do
divi.divisor.1 = 1; divi.0 = 1
return 1
end
/* Euclid's method */
a = 1; divi.left.1 = 1; b = 1; divi.right.1 = x
m = x//2
do j = 2+m by 1+m while j*j < x
if x//j = 0 then do
a = a+1; divi.left.a = j; b = b+1; divi.right.b = x%j
end
end
if j*j = x then do
a = a+1; divi.left.a = j
end
/* Save in table */
n = 0
do i = 1 to a
n = n+1; divi.divisor.n = divi.left.i
end
do i = b by -1 to 1
n = n+1; divi.divisor.n = divi.right.i
end
divi.0 = n
/* Return number of divisors */
return n
include Functions
include Numbers
include AbendThis version is slightly slower than both previous ones, due to the storage of all values in a stem. Running with parameters 1,200 gives:
REXX-ooRexx_5.0.0(MT)_64-bit 6.05 23 Dec 2022 Factors of an integer 1 has 1 divisors: 1 2 has 2 divisors: 1 2 3 has 2 divisors: 1 3 4 has 3 divisors: 1 2 4 5 has 2 divisors: 1 5 6 has 4 divisors: 1 2 3 6 7 has 2 divisors: 1 7 8 has 4 divisors: 1 2 4 8 9 has 3 divisors: 1 3 9 10 has 4 divisors: 1 2 5 10 11 has 2 divisors: 1 11 12 has 6 divisors: 1 2 3 4 6 12 13 has 2 divisors: 1 13 14 has 4 divisors: 1 2 7 14 15 has 4 divisors: 1 3 5 15 16 has 5 divisors: 1 2 4 8 16 17 has 2 divisors: 1 17 18 has 6 divisors: 1 2 3 6 9 18 19 has 2 divisors: 1 19 20 has 6 divisors: 1 2 4 5 10 20 21 has 4 divisors: 1 3 7 21 22 has 4 divisors: 1 2 11 22 23 has 2 divisors: 1 23 24 has 8 divisors: 1 2 3 4 6 8 12 24 25 has 3 divisors: 1 5 25 26 has 4 divisors: 1 2 13 26 27 has 4 divisors: 1 3 9 27 28 has 6 divisors: 1 2 4 7 14 28 29 has 2 divisors: 1 29 30 has 8 divisors: 1 2 3 5 6 10 15 30 31 has 2 divisors: 1 31 32 has 6 divisors: 1 2 4 8 16 32 33 has 4 divisors: 1 3 11 33 34 has 4 divisors: 1 2 17 34 35 has 4 divisors: 1 5 7 35 36 has 9 divisors: 1 2 3 4 6 9 12 18 36 37 has 2 divisors: 1 37 38 has 4 divisors: 1 2 19 38 39 has 4 divisors: 1 3 13 39 40 has 8 divisors: 1 2 4 5 8 10 20 40 41 has 2 divisors: 1 41 42 has 8 divisors: 1 2 3 6 7 14 21 42 43 has 2 divisors: 1 43 44 has 6 divisors: 1 2 4 11 22 44 45 has 6 divisors: 1 3 5 9 15 45 46 has 4 divisors: 1 2 23 46 47 has 2 divisors: 1 47 48 has 10 divisors: 1 2 3 4 6 8 12 16 24 48 49 has 3 divisors: 1 7 49 50 has 6 divisors: 1 2 5 10 25 50 51 has 4 divisors: 1 3 17 51 52 has 6 divisors: 1 2 4 13 26 52 53 has 2 divisors: 1 53 54 has 8 divisors: 1 2 3 6 9 18 27 54 55 has 4 divisors: 1 5 11 55 56 has 8 divisors: 1 2 4 7 8 14 28 56 57 has 4 divisors: 1 3 19 57 58 has 4 divisors: 1 2 29 58 59 has 2 divisors: 1 59 60 has 12 divisors: 1 2 3 4 5 6 10 12 15 20 30 60 61 has 2 divisors: 1 61 62 has 4 divisors: 1 2 31 62 63 has 6 divisors: 1 3 7 9 21 63 64 has 7 divisors: 1 2 4 8 16 32 64 65 has 4 divisors: 1 5 13 65 66 has 8 divisors: 1 2 3 6 11 22 33 66 67 has 2 divisors: 1 67 68 has 6 divisors: 1 2 4 17 34 68 69 has 4 divisors: 1 3 23 69 70 has 8 divisors: 1 2 5 7 10 14 35 70 71 has 2 divisors: 1 71 72 has 12 divisors: 1 2 3 4 6 8 9 12 18 24 36 72 73 has 2 divisors: 1 73 74 has 4 divisors: 1 2 37 74 75 has 6 divisors: 1 3 5 15 25 75 76 has 6 divisors: 1 2 4 19 38 76 77 has 4 divisors: 1 7 11 77 78 has 8 divisors: 1 2 3 6 13 26 39 78 79 has 2 divisors: 1 79 80 has 10 divisors: 1 2 4 5 8 10 16 20 40 80 81 has 5 divisors: 1 3 9 27 81 82 has 4 divisors: 1 2 41 82 83 has 2 divisors: 1 83 84 has 12 divisors: 1 2 3 4 6 7 12 14 21 28 42 84 85 has 4 divisors: 1 5 17 85 86 has 4 divisors: 1 2 43 86 87 has 4 divisors: 1 3 29 87 88 has 8 divisors: 1 2 4 8 11 22 44 88 89 has 2 divisors: 1 89 90 has 12 divisors: 1 2 3 5 6 9 10 15 18 30 45 90 91 has 4 divisors: 1 7 13 91 92 has 6 divisors: 1 2 4 23 46 92 93 has 4 divisors: 1 3 31 93 94 has 4 divisors: 1 2 47 94 95 has 4 divisors: 1 5 19 95 96 has 12 divisors: 1 2 3 4 6 8 12 16 24 32 48 96 97 has 2 divisors: 1 97 98 has 6 divisors: 1 2 7 14 49 98 99 has 6 divisors: 1 3 9 11 33 99 100 has 9 divisors: 1 2 4 5 10 20 25 50 100 101 has 2 divisors: 1 101 102 has 8 divisors: 1 2 3 6 17 34 51 102 103 has 2 divisors: 1 103 104 has 8 divisors: 1 2 4 8 13 26 52 104 105 has 8 divisors: 1 3 5 7 15 21 35 105 106 has 4 divisors: 1 2 53 106 107 has 2 divisors: 1 107 108 has 12 divisors: 1 2 3 4 6 9 12 18 27 36 54 108 109 has 2 divisors: 1 109 110 has 8 divisors: 1 2 5 10 11 22 55 110 111 has 4 divisors: 1 3 37 111 112 has 10 divisors: 1 2 4 7 8 14 16 28 56 112 113 has 2 divisors: 1 113 114 has 8 divisors: 1 2 3 6 19 38 57 114 115 has 4 divisors: 1 5 23 115 116 has 6 divisors: 1 2 4 29 58 116 117 has 6 divisors: 1 3 9 13 39 117 118 has 4 divisors: 1 2 59 118 119 has 4 divisors: 1 7 17 119 120 has 16 divisors: 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 121 has 3 divisors: 1 11 121 122 has 4 divisors: 1 2 61 122 123 has 4 divisors: 1 3 41 123 124 has 6 divisors: 1 2 4 31 62 124 125 has 4 divisors: 1 5 25 125 126 has 12 divisors: 1 2 3 6 7 9 14 18 21 42 63 126 127 has 2 divisors: 1 127 128 has 8 divisors: 1 2 4 8 16 32 64 128 129 has 4 divisors: 1 3 43 129 130 has 8 divisors: 1 2 5 10 13 26 65 130 131 has 2 divisors: 1 131 132 has 12 divisors: 1 2 3 4 6 11 12 22 33 44 66 132 133 has 4 divisors: 1 7 19 133 134 has 4 divisors: 1 2 67 134 135 has 8 divisors: 1 3 5 9 15 27 45 135 136 has 8 divisors: 1 2 4 8 17 34 68 136 137 has 2 divisors: 1 137 138 has 8 divisors: 1 2 3 6 23 46 69 138 139 has 2 divisors: 1 139 140 has 12 divisors: 1 2 4 5 7 10 14 20 28 35 70 140 141 has 4 divisors: 1 3 47 141 142 has 4 divisors: 1 2 71 142 143 has 4 divisors: 1 11 13 143 144 has 15 divisors: 1 2 3 4 6 8 9 12 16 18 24 36 48 72 144 145 has 4 divisors: 1 5 29 145 146 has 4 divisors: 1 2 73 146 147 has 6 divisors: 1 3 7 21 49 147 148 has 6 divisors: 1 2 4 37 74 148 149 has 2 divisors: 1 149 150 has 12 divisors: 1 2 3 5 6 10 15 25 30 50 75 150 151 has 2 divisors: 1 151 152 has 8 divisors: 1 2 4 8 19 38 76 152 153 has 6 divisors: 1 3 9 17 51 153 154 has 8 divisors: 1 2 7 11 14 22 77 154 155 has 4 divisors: 1 5 31 155 156 has 12 divisors: 1 2 3 4 6 12 13 26 39 52 78 156 157 has 2 divisors: 1 157 158 has 4 divisors: 1 2 79 158 159 has 4 divisors: 1 3 53 159 160 has 12 divisors: 1 2 4 5 8 10 16 20 32 40 80 160 161 has 4 divisors: 1 7 23 161 162 has 10 divisors: 1 2 3 6 9 18 27 54 81 162 163 has 2 divisors: 1 163 164 has 6 divisors: 1 2 4 41 82 164 165 has 8 divisors: 1 3 5 11 15 33 55 165 166 has 4 divisors: 1 2 83 166 167 has 2 divisors: 1 167 168 has 16 divisors: 1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168 169 has 3 divisors: 1 13 169 170 has 8 divisors: 1 2 5 10 17 34 85 170 171 has 6 divisors: 1 3 9 19 57 171 172 has 6 divisors: 1 2 4 43 86 172 173 has 2 divisors: 1 173 174 has 8 divisors: 1 2 3 6 29 58 87 174 175 has 6 divisors: 1 5 7 25 35 175 176 has 10 divisors: 1 2 4 8 11 16 22 44 88 176 177 has 4 divisors: 1 3 59 177 178 has 4 divisors: 1 2 89 178 179 has 2 divisors: 1 179 180 has 18 divisors: 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 181 has 2 divisors: 1 181 182 has 8 divisors: 1 2 7 13 14 26 91 182 183 has 4 divisors: 1 3 61 183 184 has 8 divisors: 1 2 4 8 23 46 92 184 185 has 4 divisors: 1 5 37 185 186 has 8 divisors: 1 2 3 6 31 62 93 186 187 has 4 divisors: 1 11 17 187 188 has 6 divisors: 1 2 4 47 94 188 189 has 8 divisors: 1 3 7 9 21 27 63 189 190 has 8 divisors: 1 2 5 10 19 38 95 190 191 has 2 divisors: 1 191 192 has 14 divisors: 1 2 3 4 6 8 12 16 24 32 48 64 96 192 193 has 2 divisors: 1 193 194 has 4 divisors: 1 2 97 194 195 has 8 divisors: 1 3 5 13 15 39 65 195 196 has 9 divisors: 1 2 4 7 14 28 49 98 196 197 has 2 divisors: 1 197 198 has 12 divisors: 1 2 3 6 9 11 18 22 33 66 99 198 199 has 2 divisors: 1 199 200 has 12 divisors: 1 2 4 5 8 10 20 25 40 50 100 200 0.016 seconds
Ring
nArray = list(100)
n = 45
j = 0
for i = 1 to n
if n % i = 0 j = j + 1 nArray[j] = i ok
next
see "Factors of " + n + " = "
for i = 1 to j
see "" + nArray[i] + " "
nextRPL
≪ → n
≪ { } DUP 1 n √ FOR d
IF n d MOD NOT
THEN
d + n d /
IF DUP d ≠ THEN ROT + SWAP ELSE DROP END
END
NEXT
SWAP +
≫ ≫
'FACTS' STO
45 FACTS 53 FACTS 64 FACTS
- Output:
3: { 1 3 5 9 15 45 }
2: { 1 53 }
1: { 1 2 4 8 16 32 64 }
Ruby
class Integer
def factors() (1..self).select { |n| (self % n).zero? } end
end
p 45.factors[1, 3, 5, 9, 15, 45]
As we only have to loop up to , we can write
class Integer
def factors
1.upto(Integer.sqrt(self)).select {|i| (self % i).zero?}.inject([]) do |f, i|
f << self/i unless i == self/i
f << i
end.sort
end
end
[45, 53, 64].each {|n| puts "#{n} : #{n.factors}"}- Output:
45 : [1, 3, 5, 9, 15, 45] 53 : [1, 53] 64 : [1, 2, 4, 8, 16, 32, 64]
Using the prime library
require 'prime'
def factors m
return [1] if 1==m
primes, powers = Prime.prime_division(m).transpose
ranges = powers.map{|n| (0..n).to_a}
ranges[0].product( *ranges[1..-1] ).
map{|es| primes.zip(es).map{|p,e| p**e}.reduce :*}.
sort
end
[1, 7, 45, 100].each{|n| p factors n}Output:
[1] [1, 7] [1, 3, 5, 9, 15, 45] [1, 2, 4, 5, 10, 20, 25, 50, 100]
Rust
fn main() {
assert_eq!(vec![1, 2, 4, 5, 10, 10, 20, 25, 50, 100], factor(100)); // asserts that two expressions are equal to each other
assert_eq!(vec![1, 101], factor(101));
}
fn factor(num: i32) -> Vec<i32> {
let mut factors: Vec<i32> = Vec::new(); // creates a new vector for the factors of the number
for i in 1..((num as f32).sqrt() as i32 + 1) {
if num % i == 0 {
factors.push(i); // pushes smallest factor to factors
factors.push(num/i); // pushes largest factor to factors
}
}
factors.sort(); // sorts the factors into numerical order for viewing purposes
factors // returns the factors
}Alternative functional version:
fn factor(n: i32) -> Vec<i32> {
(1..=n).filter(|i| n % i == 0).collect()
}Sather
class MAIN is
factors!(n :INT):INT is
yield 1;
loop i ::= 2.upto!( n.flt.sqrt.int );
if n%i = 0 then
yield i;
if (i*i) /= n then
yield n / i;
end;
end;
end;
yield n;
end;
main is
a :ARRAY{INT} := |3135, 45, 64, 53, 45, 81|;
loop l ::= a.elt!;
#OUT + "factors of " + l + ": ";
loop ri ::= factors!(l);
#OUT + ri + " ";
end;
#OUT + "\n";
end;
end;
end;Scala
Brute force approach:
def factors(num: Int) = {
(1 to num).filter { divisor =>
num % divisor == 0
}
}Brute force until sqrt(num) is enough, the code above can be edited as follows (Scala 3 enabled)
def factors(num: Int) = {
val list = (1 to math.sqrt(num).floor.toInt).filter(num % _ == 0)
list ++ list.reverse.dropWhile(d => d*d == num).map(num / _)
}Scheme
This implementation uses a naive trial division algorithm.
(define (factors n)
(define (*factors d)
(cond ((> d n) (list))
((= (modulo n d) 0) (cons d (*factors (+ d 1))))
(else (*factors (+ d 1)))))
(*factors 1))
(display (factors 1111111))
(newline)- Output:
(1 239 4649 1111111)
Seed7
$ include "seed7_05.s7i";
const proc: writeFactors (in integer: number) is func
local
var integer: testNum is 0;
begin
write("Factors of " <& number <& ": ");
for testNum range 1 to sqrt(number) do
if number rem testNum = 0 then
if testNum <> 1 then
write(", ");
end if;
write(testNum);
if testNum <> number div testNum then
write(", " <& number div testNum);
end if;
end if;
end for;
writeln;
end func;
const proc: main is func
local
const array integer: numsToFactor is [] (45, 53, 64);
var integer: number is 0;
begin
for number range numsToFactor do
writeFactors(number);
end for;
end func;- Output:
Factors of 45: 1, 45, 3, 15, 5, 9 Factors of 53: 1, 53 Factors of 64: 1, 64, 2, 32, 4, 16, 8
SequenceL
Brute Force Method
A simple brute force method using an indexed partial function as a filter.
Factors(num(0))[i] := i when num mod i = 0 foreach i within 1 ... num;Slightly More Efficient Method
A slightly more efficient method, only going up to the sqrt(n).
Factors(num(0)) :=
let
factorPairs[i] :=
[i] when i = sqrt(num)
else
[i, num/i] when num mod i = 0
foreach i within 1 ... floor(sqrt(num));
in
join(factorPairs);Sidef
Built-in:
say divisors(97) #=> [1, 97]
say divisors(2695) #=> [1, 5, 7, 11, 35, 49, 55, 77, 245, 385, 539, 2695]Trial-division (slow for large n):
func divisors(n) {
gather {
{ |d|
take(d, n//d) if d.divides(n)
} << 1..n.isqrt
}.sort.uniq
}
[53, 64, 32766].each {|n|
say "divisors(#{n}): #{divisors(n)}"
}- Output:
divisors(53): [1, 53] divisors(64): [1, 2, 4, 8, 16, 32, 64] divisors(32766): [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766]
Slate
n@(Integer traits) primeFactors
[
[| :result |
result nextPut: 1.
n primesDo: [| :prime | result nextPut: prime]] writingAs: {}
].where primesDo: is a part of the standard numerics library:
n@(Integer traits) primesDo: block
"Decomposes the Integer into primes, applying the block to each (in increasing
order)."
[| div next remaining |
div: 2.
next: 3.
remaining: n.
[[(remaining \\ div) isZero]
whileTrue:
[block applyTo: {div}.
remaining: remaining // div].
remaining = 1] whileFalse:
[div: next.
next: next + 2] "Just looks at the next odd integer."
].Smalltalk
Copied from the Python example, but code added to the Integer built in class:
Integer>>factors
| a |
a := OrderedCollection new.
1 to: (self / 2) do: [ :i |
((self \\ i) = 0) ifTrue: [ a add: i ] ].
a add: self.
^aThen use as follows:
59 factors -> an OrderedCollection(1 59)
120 factors -> an OrderedCollection(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120)Standard ML
Need to print the list because Standard ML truncates the display of longer returned lists.
fun printIntList ls =
(
List.app (fn n => print(Int.toString n ^ " ")) ls;
print "\n"
);
fun factors n =
let
fun factors'(n, k) =
if k > n then
[]
else if n mod k = 0 then
k :: factors'(n, k+1)
else
factors'(n, k+1)
in
factors'(n,1)
end;Call:
printIntList(factors 12345)
printIntList(factors 120)- Output:
1 3 5 15 823 2469 4115 12345 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60
Swift
Simple implementation:
func factors(n: Int) -> [Int] {
return filter(1...n) { n % $0 == 0 }
}More efficient implementation:
import func Darwin.sqrt
func sqrt(x:Int) -> Int { return Int(sqrt(Double(x))) }
func factors(n: Int) -> [Int] {
var result = [Int]()
for factor in filter (1...sqrt(n), { n % $0 == 0 }) {
result.append(factor)
if n/factor != factor { result.append(n/factor) }
}
return sorted(result)
}Call:
println(factors(4))
println(factors(1))
println(factors(25))
println(factors(63))
println(factors(19))
println(factors(768))- Output:
[1, 2, 4] [1] [1, 5, 25] [1, 3, 7, 9, 21, 63] [1, 19] [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768]
Tailspin
[1..351 -> \(when <?(351 mod $ <=0>)> do $! \)] -> !OUT::writev0.5
[1..351 -> if <|?(351 mod $ matches <|=0>)>] !- Output:
[1, 3, 9, 13, 27, 39, 117, 351]
Tcl
proc factors {n} {
set factors {}
for {set i 1} {$i <= sqrt($n)} {incr i} {
if {$n % $i == 0} {
lappend factors $i [expr {$n / $i}]
}
}
return [lsort -unique -integer $factors]
}
puts [factors 64]
puts [factors 45]
puts [factors 53]- Output:
1 2 4 8 16 32 64 1 3 5 9 15 45 1 53
Uiua
Factors ← ◴⊂⟜(⇌÷)⊸(▽:⟜≡(=0◿)⊙¤⊸(↘1⇡+1⌊√))
⍚Factors {45 53 64}- Output:
{[1 3 5 9 15 45] [1 53] [1 2 4 8 16 32 64]}
UNIX Shell
This should work in all Bourne-compatible shells, assuming the system has both sort and at least one of bc or dc.
factor() {
r=`echo "sqrt($1)" | bc` # or `echo $1 v p | dc`
i=1
while [ $i -lt $r ]; do
if [ `expr $1 % $i` -eq 0 ]; then
echo $i
expr $1 / $i
fi
i=`expr $i + 1`
done | sort -nu
}Ursa
This program takes an integer from the command line and outputs its factors.
decl int n
set n (int args<1>)
decl int i
for (set i 1) (< i (+ (/ n 2) 1)) (inc i)
if (= (mod n i) 0)
out i " " console
end if
end for
out n endl consoleUrsala
The simple way:
#import std
#import nat
factors "n" = (filter not remainder/"n") nrange(1,"n")The complicated way:
factors "n" = nleq-<&@s <.~&r,quotient>*= "n"-* (not remainder/"n")*~ nrange(1,root("n",2))Another idea would be to approximate an upper bound for the square root of "n" with some bit twiddling such as &!*K31 "n", which evaluates to a binary number of all 1's half the width of "n" rounded up, and another would be to use the division function to get the quotient and remainder at the same time. Combining these ideas, losing the dummy variable, and cleaning up some other cruft, we have
factors = nleq-<&@rrZPFLs+ ^(~&r,division)^*D/~& nrange/1+ &!*K31where nleq-<& isn't strictly necessary unless an ordered list is required.
#cast %nL
example = factors 100- Output:
<1,2,4,5,10,20,25,50,100>
Verilog
module main;
integer i, n;
initial begin
n = 45;
$write(n, " =>");
for(i = 1; i <= n / 2; i = i + 1) if(n % i == 0) $write(i);
$display(n);
$finish ;
end
endmodule- Output:
45 => 1 3 5 9 15 45
Wortel
@let {
factors1 &n !-\%%n @to n
factors_tacit @(\\%% !- @to)
[[
!factors1 10
!factors_tacit 100
!factors1 720
]]
}Returns:
[ [1 2 5 10] [1 2 4 5 10 20 25 50 100] [1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720] ]
V (Vlang)
fn main() {
mut arr := []int{len: 100}
mut n, mut j := 45, 0
for i in 1..n + 1 {
if n % i == 0 {
j++
arr[j] = i
}
}
print("Factors of ${n} = ")
for i in 1..j + 1 {print(" ${arr[i]} ")}
}- Output:
Factors of 45 = 1 3 5 9 15 45
Wren
import "./fmt" for Fmt
import "./math" for Int
var a = [11, 21, 32, 45, 67, 96, 159, 723, 1024, 5673, 12345, 32767, 123459, 999997]
System.print("The factors of the following numbers are:")
for (e in a) Fmt.print("$6d => $n", e, Int.divisors(e))- Output:
The factors of the following numbers are:
11 => [1, 11]
21 => [1, 3, 7, 21]
32 => [1, 2, 4, 8, 16, 32]
45 => [1, 3, 5, 9, 15, 45]
67 => [1, 67]
96 => [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96]
159 => [1, 3, 53, 159]
723 => [1, 3, 241, 723]
1024 => [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]
5673 => [1, 3, 31, 61, 93, 183, 1891, 5673]
12345 => [1, 3, 5, 15, 823, 2469, 4115, 12345]
32767 => [1, 7, 31, 151, 217, 1057, 4681, 32767]
123459 => [1, 3, 7, 21, 5879, 17637, 41153, 123459]
999997 => [1, 757, 1321, 999997]
X86 Assembly
section .bss
factorArr resd 250 ;big buffer against seg fault
section .text
global _main
_main:
mov ebp, esp; for correct debugging
mov eax, 0x7ffffffe ;number of which we want to know the factors, max num this program works with
mov ebx, eax ;save eax
mov ecx, 1 ;n, factor we test for
mov [factorArr], dword 0
looping:
mov eax, ebx ;restore eax
xor edx, edx ;clear edx
div ecx
cmp edx, 0 ;test if our number % n == 0
jne next
mov edx, [factorArr] ;if yes, we increment the size of the array and append n
inc edx
mov [factorArr+edx*4], ecx ;appending n
mov [factorArr], edx ;storing the new size
next:
mov eax, ecx
cmp eax, ebx ;is n bigger then our number ?
jg end ;if yes we end
inc ecx
jmp looping
end:
mov ecx, factorArr ;pass arr address by ecx
xor eax, eax ;clear eax
mov esp, ebp ;garbage collecting
retXPL0
include c:\cxpl\codes;
int N0, N, F;
[N0:= 1;
repeat IntOut(0, N0); Text(0, " = ");
F:= 2; N:= N0;
repeat if rem(N/F) = 0 then
[if N # N0 then Text(0, " * ");
IntOut(0, F);
N:= N/F;
]
else F:= F+1;
until F>N;
if N0=1 then IntOut(0, 1); \1 = 1
CrLf(0);
N0:= N0+1;
until KeyHit;
]- Output:
1 = 1 2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 12 = 2 * 2 * 3 13 = 13 14 = 2 * 7 15 = 3 * 5 16 = 2 * 2 * 2 * 2 17 = 17 18 = 2 * 3 * 3 . . . 57086 = 2 * 17 * 23 * 73 57087 = 3 * 3 * 6343 57088 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 223 57089 = 57089 57090 = 2 * 3 * 5 * 11 * 173 57091 = 37 * 1543 57092 = 2 * 2 * 7 * 2039 57093 = 3 * 19031 57094 = 2 * 28547 57095 = 5 * 19 * 601 57096 = 2 * 2 * 2 * 3 * 3 * 13 * 61 57097 = 57097
zkl
fcn f(n){ (1).pump(n.toFloat().sqrt(), List,
'wrap(m){((n % m)==0) and T(m,n/m) or Void.Skip}) }
fcn g(n){ [[(m); [1..n.toFloat().sqrt()],'{n%m==0}; '{T(m,n/m)} ]] } // list comprehension- Output:
zkl: f(45) L(L(1,45),L(3,15),L(5,9)) zkl: g(45) L(L(1,45),L(3,15),L(5,9))
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