Factors of an integer
Compute the factors of a positive integer.
You are encouraged to solve this task according to the task description, using any language you may know.
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
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- Task
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
0815
<lang 0815> <:1:~>|~#:end:>~x}:str:/={^:wei:~%x<:a:x=$~ =}:wei:x<:1:+{>~>x=-#:fin:^:str:}:fin:{{~% </lang>
360 Assembly
Very compact version. <lang 360asm>* 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</lang>
- Output:
1 3 5 15 823 2469 4115 12345
ACL2
<lang Lisp>(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))</lang>
ActionScript
<lang 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; }</lang>
Ada
<lang 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;</lang>
Aikido
<lang 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))</lang>
ALGOL 68
Note: The following implements generators, eliminating the need of declaring arbitrarily long int arrays for caching. <lang algol68>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</lang>
- Output:
+45: 1, 45, 3, 15, 5, 9 +53: 1, 53 +64: 1, 64, 2, 32, 4, 16, 8
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 this 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.) <lang algol> BEGIN
COMMENT ALGOL-M PROGRAM TO DISPLAY THE FACTORS OF AN INTEGER
INTEGER I, N, LIMIT, FOUND, START, DELTA; STRING(1) ANOTHER;
COMMENT COMPUTE P MOD Q; INTEGER FUNCTION MOD (P, Q); INTEGER P, Q; BEGIN
MOD := P - Q * (P / Q);
END;
COMMENT MAIN PROGRAM BEGINS HERE; ANOTHER := "Y"; WHILE ANOTHER = "Y" OR ANOTHER = "y" DO
BEGIN WRITE ("Number to factor:"); READ (N); 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 / START; WHILE I <= LIMIT DO BEGIN IF MOD(N, I) = 0 THEN BEGIN WRITE (I); FOUND := FOUND + 1; END; I := I + DELTA; IF FOUND = 0 THEN LIMIT := N / I; END;
IF FOUND = 0 THEN WRITE ("None - the number is prime."); WRITE(" "); WRITE("Do another (y/n)?"); READ (ANOTHER); END;
WRITE (" "); WRITE ("Goodbye"); END </lang>
ALGOL W
<lang algolw>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.</lang>
- 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
APL
<lang 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</lang>
AppleScript
<lang AppleScript>-- integerFactors :: Int -> [Int] on integerFactors(n)
if n = 1 then {1} 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</lang>
- Output:
<lang AppleScript>{1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}</lang>
Arc
<lang 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))) </lang>
- Output:
<lang Arc> '( (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) ) </lang>
ARM Assembly
<lang 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 0x66666667
</lang>
AutoHotkey
<lang 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
}</lang>
- Output:
1,3,5,9,15,45 1,53 1,2,4,8,16,32,64
AutoIt
<lang 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</lang>
- Output:
Factors of 45 are: 1, 3, 5, 9, 15, 45
AWK
<lang 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")
} </lang>
- 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
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). <lang qbasic>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) FOR L1 = 0 TO UBOUND(factors) - 1 factors(L1) = tmp(L1) NEXT factors(UBOUND(factors)) = L0 END IF NEXT
END SUB</lang>
- 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
IS-BASIC
<lang 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</lang>
Sinclair ZX81 BASIC
<lang basic>10 INPUT N 20 FOR I=1 TO N 30 IF N/I=INT (N/I) THEN PRINT I;" "; 40 NEXT I</lang>
- Input:
315
- Output:
1 3 5 7 9 15 35 45 63 105 315
Batch File
Command line version: <lang dos>@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</lang>
- 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: <lang dos>@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</lang>
- 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
BBC BASIC
<lang bbcbasic> 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$(L$))</lang>
- 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
bc
<lang 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)
}</lang>
Befunge
<lang Befunge>10:p&v: >:0:g%#v_0:g\:0:g/\v
>:0:g:*`| > >0:g1+0:p >:0:g:*-#v_0:g\>$>:!#@_.v > ^ ^ ," "<</lang>
Burlesque
<lang burlesque>blsq ) 32767 fc {1 7 31 151 217 1057 4681 32767}</lang>
C
<lang 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;
}</lang>
Prime factoring
<lang C>#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; }</lang>
- 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++
<lang Cpp>#include <iostream>
- include <vector>
- include <algorithm>
- include <iterator>
std::vector<int> GenerateFactors(int n) {
std::vector<int> factors; factors.push_back(1); factors.push_back(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 " << SampleNumbers[i] << " are:\n"; std::copy(factors.begin(), factors.end(), std::ostream_iterator<int>(std::cout, "\n")); std::cout << std::endl; }
}</lang>
C#
C# 3.0 <lang csharp>using System; using System.Linq; using System.Collections.Generic;
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())); }
}</lang>
C# 1.0 <lang csharp>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); }</lang>
- Output:
Number: 32434243 For 1 through 5695 Found: 1. 32434243 / 1 = 32434243 Found: 307. 32434243 / 307 = 105649 Done.
Ceylon
<lang 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)``"); } }</lang>
Chapel
Inspired by the Clojure solution: <lang chapel>iter factors(n) { for i in 1..floor(sqrt(n)):int { if n % i == 0 then { yield i; yield n / i; } } }</lang>
Clojure
<lang lisp>(defn factors [n] (filter #(zero? (rem n %)) (range 1 (inc n))))
(print (factors 45))</lang>
(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. <lang lisp>(defn factors [n]
(into (sorted-set) (mapcat (fn [x] [x (/ n x)]) (filter #(zero? (rem n %)) (range 1 (inc (Math/sqrt n)))) )))</lang>
Same idea, using for comprehensions. <lang lisp>(defn factors [n]
(into (sorted-set) (reduce concat (for [x (range 1 (inc (Math/sqrt n))) :when (zero? (rem n x))] [x (/ n x)]))))</lang>
COBOL
<lang 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.
</lang>
CoffeeScript
<lang 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</lang>
- 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.
<lang lisp>(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)))))</lang>
D
Procedural Style
<lang d>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);
}</lang>
- Output:
[1, 3, 5, 9, 15, 45] [1, 53] [1, 2, 4, 8, 16, 32, 64] [1, 239, 4649, 1111111]
Functional Style
<lang d>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;
}</lang>
- 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)); }
Dyalect
<lang Dyalect>func Iterator.where(pred) {
for x in this when pred(x) { yield x }
}
func Integer.factors() {
(1..this).where(this % $0 == 0)
}
for x in 45.factors() {
print(x)
}</lang>
Output:
1 3 5 9 15 45
E
<lang e>def factors(x :(int > 0)) {
var xfactors := [] for f ? (x % f <=> 0) in 1..x { xfactors with= f } return xfactors
}</lang>
EasyLang
<lang>n = 720 for i = 1 to n
if n mod i = 0 factors[] &= i .
. print factors[]</lang>
EchoLisp
prime-factors gives the list of n's prime-factors. We mix them to get all the factors. <lang scheme>
- 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)))))) </lang>
- Output:
<lang scheme> (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)
</lang>
Ela
Using higher-order function
<lang ela>open list
factors m = filter (\x -> m % x == 0) [1..m]</lang>
Using comprehension
<lang ela>factors m = [x \\ x <- [1..m] | m % x == 0]</lang>
Elixir
<lang 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) </lang>
- 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
Erlang
with Built in fuctions
<lang erlang>factors(N) ->
[I || I <- lists:seq(1,trunc(N/2)), N rem I == 0]++[N].</lang>
Recursive
Another, less concise, but faster version <lang erlang>
-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)).
</lang>
- 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
<lang 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 </lang>
- 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
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. <lang fsharp>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
}</lang>
Prime factoring
<lang fsharp> [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 "");;</lang>
- 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
<lang false>[1[\$@$@-][\$@$@$@$@\/*=[$." "]?1+]#.%]f: 45f;! 53f;! 64f;!</lang>
Fish
<lang Fish>0v
>i:0(?v'0'%+a* >~a,:1:>r{% ?vr:nr','ov ^:&:;?(&:+1r:< <
</lang> 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. <lang Forth>: 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</lang>
Fortran
<lang 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</lang>
FreeBASIC
<lang 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</lang>
- 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
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:
<lang frink>allFactors[n]</lang>
FunL
Function to compute set of factors: <lang funl>def factors( n ) = {d | d <- 1..n if d|n}</lang>
Test: <lang funl>for x <- [103, 316, 519, 639, 760]
println( 'The set of factors of ' + x + ' is ' + factors(x) )</lang>
- 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
<lang futurebasic> include "ConsoleWindow"
clear local mode local fn IntegerFactors( f as long ) as Str255 dim as long i, s, l(100), c : c = 0 dim as Str255 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 = factorStr + str$(l(i)) + "," else factorStr = factorStr + str$(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 ) </lang>
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
GAP
<lang 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 ]</lang>
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. <lang go>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))
}</lang>
- 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
<lang 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}")
}</lang>
- 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: <lang groovy>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]
}</lang>
Test: <lang groovy>((1..30) + [333333]).each { println ([number:it, factors:factorize(it)]) }</lang>
- 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 <lang Haskell>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</lang>
Returns list of factors out of order, e.g.:
<Lang haskell>~> factors 42 [1,7,3,21,2,14,6,42]</lang>
Or, prime decomposition task can be used (although, a trial division-only version will become very slow for large primes),
<lang haskell>import Data.List (group) primePowerFactors = map (\x-> (head x, length x)) . group . factorize</lang>
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:
<lang Haskell>import Control.Arrow ((&&&)) import Data.Bool (bool)
integerFactors :: Int -> [Int] integerFactors n =
bool -- For perfect squares, `tail` excludes cofactor of square root (lows ++ (quot n <$> bool id tail (n == intSquared) (reverse lows))) [] (n < 1) where (intSquared, lows) = (^ 2) &&& (filter ((0 ==) . rem n) . enumFromTo 1) $ floor (sqrt $ fromIntegral n)
main :: IO () main = print $ integerFactors 600</lang>
- 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: <lang Haskell>factorsNaive n =
[ i | i <- [1 .. n] , mod n i == 0 ]</lang>
<lang Haskell>~> factorsNaive 25 [1,5,25]</lang>
Factor, cofactor. Get the list of factor–cofactor pairs sorted, for a quadratic speedup: <lang Haskell>import Data.List (sort)
factorsCo n =
sort [ i | i <- [1 .. floor (sqrt (fromIntegral n))] , (d, 0) <- [divMod n i] , i <- i : [ d | d > i ] ]</lang>
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: <lang Haskell>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 ]</lang>
Testing: <lang Haskell>*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)</lang>
HicEst
<lang hicest> DLG(NameEdit=N, TItle='Enter an integer')
DO i = 1, N^0.5 IF( MOD(N,i) == 0) WRITE() i, N/i ENDDO
END</lang>
Icon and Unicon
<lang Icon>procedure main(arglist) numbers := arglist ||| [ 32767, 45, 53, 64, 100] # combine command line provided and default set of values every writes(lf,"factors of ",i := !numbers,"=") & writes(divisors(i)," ") do lf := "\n" end
link factors</lang>
- 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
J
The "brute force" approach is the most concise:
<lang J>foi=: [: I. 0 = (|~ i.@>:)</lang>
Example use:
<lang J> foi 40 1 2 4 5 8 10 20 40</lang>
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. <lang J>q: 40
2 2 2 5</lang>
Alternatively, q: can produce provide a table of the exponents of the unique relevant prime factors <lang J> __ q: 420 2 3 5 7 2 1 1 1</lang>
With this, we can form lists of each of the potential relevant powers of each of these prime factors <lang J> (^ i.@>:)&.>/ __ q: 420 ┌─────┬───┬───┬───┐ │1 2 4│1 3│1 5│1 7│ └─────┴───┴───┴───┘</lang>
From here, it's a simple matter (*/&>@{
) to compute all possible factors of the original number
<lang J>factrs=: */&>@{@((^ i.@>:)&.>/)@q:~&__
factrs 40 1 5 2 10 4 20 8 40</lang>
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:
<lang J> factors=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__
factors 420
1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 140 210 420</lang>
A less efficient, but concise variation on this theme:
<lang J> ~.,*/&> { 1 ,&.> q: 40 1 5 2 10 4 20 8 40</lang>
This 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:
<lang J> 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 5.68474e8</lang>
One 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:
<lang J> 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 568474220</lang>
Another 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: <lang J>factorsOfNumber=: monad define
Y=. y"_ /:~ ~. ( , Y%]) ( #~ 0=]|Y) 1+i.>.%:y
)
factorsOfNumber 40
1 2 4 5 8 10 20 40</lang>
Another approach:
<lang J>odometer =: #: i.@(*/) factors=: (*/@:^"1 odometer@:>:)/@q:~&__</lang>
Java
<lang java5>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;
}</lang>
JavaScript
Imperative
<lang javascript>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]</lang>
Functional
ES5
Translating the naive list comprehension example from Haskell, using a list monad for the comprehension
<lang JavaScript>// 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)</lang>
Output: <lang JavaScript>[1, 2, 3, 6]</lang>
Translating the Haskell (lows and highs) example
<lang JavaScript>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])
);</lang>
Output:
<lang JavaScript>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
</lang>
ES6
<lang JavaScript>(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]);</lang>
- 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
<lang 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</lang>
- 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
<lang julia>using Primes
function factors(n)
f = [one(n)] for (p,e) in factor(n) f = reduce(vcat, [f*p^j for j in 1:e], init=f) end return length(f) == 1 ? [one(n), n] : sort!(f)
end
const examples = [28, 45, 53, 64, 6435789435768]
for n in examples
@time println("The factors of $n are: $(factors(n))")
end </lang>
- 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
<lang 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 24</lang>
Kotlin
<lang scala>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)
}</lang>
- 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
LFE
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): <lang lisp> (defun factors (n)
(list-comp ((<- i (when (== 0 (rem n i))) (lists:seq 1 (trunc (/ n 2))))) i))
</lang>
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): <lang lisp> (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)))
</lang>
- Output:
> (factors 10677106534462215678539721403561279) (104729 104729 104729 98731 98731 32579 29269 1)
Liberty BASIC
<lang lb>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</lang>
- Output:
<lang lb>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 done</lang>
A Simpler Approach
This is a somewhat simpler approach for finding the factors of smaller numbers (less than one million).
<lang lb> 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 </lang>
- 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 129 87 15873 25641 27027 30303 37037 47619 76923 90909 111111 142857 333333 999999 Enter an integer (< 1,000,000): Program complete.
Lingo
<lang 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
end</lang> <lang lingo>put factors(45) -- [1, 3, 5, 9, 15, 45] put factors(53) -- [1, 53] put factors(64) -- [1, 2, 4, 8, 16, 32, 64]</lang>
Logo
<lang logo>to factors :n
output filter [equal? 0 modulo :n ?] iseq 1 :n
end
show factors 28 ; [1 2 4 7 14 28]</lang>
Lua
<lang 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
end</lang>
M2000 Interpreter
<lang M2000 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 LikeM2000
</lang>
Maple
<lang Maple> numtheory:-divisors(n); </lang>
Mathematica / Wolfram Language
<lang Mathematica>Factorize[n_Integer] := Divisors[n]</lang>
MATLAB / Octave
<lang Matlab> 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; </lang>
- 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.
<lang maxima>(%i96) divisors(100);
(%o96) {1,2,4,5,10,20,25,50,100}</lang>
Such a function could be implemented like so: <lang maxima>divisors2(n) := map( lambda([l], lreduce("*", l)),
apply( cartesian_product, map( lambda([fac], setify(makelist(fac[1]^i, i, 0, fac[2]))), ifactors(n))));</lang>
MAXScript
<lang MAXScript> fn factors n = ( return (for i = 1 to n+1 where mod n i == 0 collect i) ) </lang>
- Output:
<lang MAXScript> 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)
</lang>
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
<lang Mercury>:- 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.</lang>
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])
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
<lang 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]</lang>
NetRexx
<lang NetRexx>/* 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 */</lang>
- 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
<lang nim>import intsets, math, algorithm
proc factors(n): seq[int] =
var fs = initIntSet() for x in 1 .. int(sqrt(float(n))): if n mod x == 0: fs.incl(x) fs.incl(n div x)
result = @[] for x in fs: result.add(x) sort(result, system.cmp[int])
echo factors(45)</lang>
Niue
<lang 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 ) </lang>
Oberon-2
Oxford Oberon-2 <lang oberon2> 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. </lang>
- Output:
1 3 41 123 4 factors
Objeck
<lang 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(); }; } }
}</lang>
OCaml
<lang ocaml>let rec range = function 0 -> [] | n -> range(n-1) @ [n]
let factors n =
List.filter (fun v -> (n mod v) = 0) (range n)</lang>
Oforth
<lang Oforth>Integer method: factors self seq filter(#[ self isMultiple ]) ;
120 factors println</lang>
- Output:
[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]
Oz
<lang 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}}</lang>
PARI/GP
<lang parigp>divisors(n)</lang>
Panda
Panda has a factor function already, it's defined as: <lang panda>fun factor(n) type integer->integer
f where n.mod(1..n=>f)==0
45.factor</lang>
Pascal
<lang 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.</lang>
- 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
small improvement
the factors are in ascending order.
<lang pascal>program factors; {Looking for extreme composite numbers: http://wwwhomes.uni-bielefeld.de/achim/highly.txt}
const
MAXFACTORCNT = 1920; //number := 3491888400;
var
FaktorList : array[0..MAXFACTORCNT] of LongWord; i, number,quot,cnt: LongWord;
begin
writeln('Enter a number between 1 and 4294967295: '); write('3491888400 is a nice choice '); readln(number);
cnt := 0; i := 1; repeat quot := number div i; if quot *i-number = 0 then begin FaktorList[cnt] := i; FaktorList[MAXFACTORCNT-cnt] := quot; inc(cnt); end; inc(i); until i> quot; writeln(number,' has ',2*cnt,' factors'); dec(cnt); For i := 0 to cnt do write(FaktorList[i],' ,'); For i := cnt downto 1 do write(FaktorList[MAXFACTORCNT-i],' ,');
{ the last without ','}
writeln(FaktorList[MAXFACTORCNT]);
end.</lang>
- Output:
Enter a number between 1 and 4294967295: 3491888400 is a nice choice 120 120 has 16 factors 1 ,2 ,3 ,4 ,5 ,6 ,8 ,10 ,12 ,15 ,20 ,24 ,30 ,40 ,60 ,120
Perl
<lang perl>sub factors {
my($n) = @_; return grep { $n % $_ == 0 }(1 .. $n);
} print join ' ',factors(64), "\n";</lang>
Or more intelligently:
<lang perl>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";</lang>
One could also use a module, e.g.:
<lang perl>use ntheory qw/divisors/; print join " ", divisors(12345678), "\n";
- Alternately something like: fordivisors { say } 12345678; </lang>
Perl 6
<lang perl6>sub factors (Int $n) { squish sort ($_, $n div $_ if $n %% $_ for 1 .. sqrt $n) }</lang>
Phix
There is a builtin factors(n), which takes an optional second parameter to include 1 and n, so eg ?factors(12345,1) displays
- Output:
{1,3,5,15,823,2469,4115,12345}
You can find the implementation of factors() and prime_factors() in builtins\pfactors.e
PHP
<lang PHP>function GetFactors($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 $factors;
}</lang>
PicoLisp
<lang PicoLisp>(de factors (N)
(filter '((D) (=0 (% N D))) (range 1 N) ) )</lang>
PILOT
<lang pilot>T :Enter a number. A :#n C :factor = 1 T :The factors of #n are:
- Loop
C :remainder = n % factor T ( remainder = 0 ) :#factor J ( factor = n ) :*Finished C :factor = factor + 1 J :*Loop
- Finished
END:</lang>
PL/I
<lang PL/I>do i = 1 to n;
if mod(n, i) = 0 then put skip list (i);
end;</lang>
PowerShell
Straightforward but slow
<lang powershell>function Get-Factor ($a) {
1..$a | Where-Object { $a % $_ -eq 0 }
}</lang>
This one uses a range of integers up to the target number and just filters it using the Where-Object
cmdlet. It's very slow though, so it is not very usable for larger numbers.
A little more clever
<lang powershell>function Get-Factor ($a) {
1..[Math]::Sqrt($a) ` | Where-Object { $a % $_ -eq 0 } ` | ForEach-Object { $_; $a / $_ } ` | Sort-Object -Unique
}</lang> 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: <lang ProDOS>editvar /newvar /value=a /userinput=1 /title=Enter an integer: do /delimspaces %% -a- >b printline Factors of -a-: -b- </lang>
Prolog
Simple Brute Force Implementation <lang Prolog> brute_force_factors( N , Fs ) :-
integer(N) , N > 0 , setof( F , ( between(1,N,F) , N mod F =:= 0 ) , Fs ) .
</lang>
A Slightly Smarter Implementation <lang Prolog> 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 ) .
</lang>
Not every Prolog has between/3
: you might need this:
<lang Prolog>
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) .
</lang>
- 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] .
PureBasic
<lang 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</lang>
- Output:
Enter integer to factorize: 96 1 2 3 4 6 8 12 16 24 32 48 96
Python
Naive and slow but simplest (check all numbers from 1 to n): <lang python>>>> def factors(n):
return [i for i in range(1, n + 1) if not n%i]</lang>
Slightly better (realize that there are no factors between n/2 and n): <lang python>>>> 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]</lang>
Much better (realize that factors come in pairs, the smaller of which is no bigger than sqrt(n)): <lang python>>>> from math import sqrt >>> def factor(n):
factors = set() for x in range(1, int(sqrt(n)) + 1): if n % x == 0: factors.add(x) factors.add(n//x) return sorted(factors)
>>> 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]</lang>
More efficient when factoring many numbers: <lang python>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 r</lang>
R
<lang R>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] }
} factors(60)</lang>
1 2 3 4 5 6 10 12 15 20 30 60
<lang R>factors(c(45, 53, 64))</lang>
[[1]] [1] 1 3 5 9 15 45 [[2]] [1] 1 53 [[3]] [1] 1 2 4 8 16 32 64
Racket
<lang 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 17ms
</lang>
REALbasic
<lang vb>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</lang>
REXX
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 factors.
It also displays a final count of the number of primes found.
<lang rexx>/*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(high)+2; numeric digits max(9, w-2); $='∞' /*decimal digits for // */
@.=left(,7); @.1="{unity}"; @.2='[prime]'; @.$=" {"$'} ' /*define some literals. */
say center('n', w) "#divisors" center('divisors', 60) /*display the header. */
say copies('═', w) "═════════" copies('═' , 60) /* " " separator. */
p#=0 /*count of prime numbers. */
do n=LO to HI by inc; divs=divisors(n); #=words(divs) /*get list of divs; # divs*/ if divs==$ then do; #=$ ; divs= ' (infinite)'; end /*handle case for infinity*/ p=@.#; if n<0 then if n\==-1 then p=@.. /* " " " negative*/ if p==@.2 then p#=p#+1 /*Prime? Then bump counter*/ say center(n, w) center('['#"]", 9) "──► " p ' ' divs end /*n*/ /* [↑] process a range of integers. */
say say left(, 17) p# ' primes were found.' /*display the number of primes found. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ divisors: procedure; 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 j*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 factors to α and ß lists.*/ end /*j*/ /* [↑] % ≡ integer division. ___*/
if j*j==x then return a j b /*Was X a square? Then insert √ x */
return a b /*return the divisors of both lists. */</lang>
output when the input used is: -6 200
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 Primes that were found: 46
Alternate Version
<lang REXX>/* 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 */</lang>
Ring
<lang 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] + " "
next </lang>
Ruby
<lang ruby>class Integer
def factors() (1..self).select { |n| (self % n).zero? } end
end p 45.factors</lang>
[1, 3, 5, 9, 15, 45]
As we only have to loop up to , we can write <lang ruby>class Integer
def factors 1.upto(Math.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}"}</lang>
- Output:
45 : [1, 3, 5, 9, 15, 45] 53 : [1, 53] 64 : [1, 2, 4, 8, 16, 32, 64]
Using the prime library
<lang ruby> 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} </lang> Output:
[1] [1, 7] [1, 3, 5, 9, 15, 45] [1, 2, 4, 5, 10, 20, 25, 50, 100]
Run BASIC
<lang runbasic>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</lang>
- Output:
Factors of 45 are 1, 3, 5, 9, 15, 45, Factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345,
Rust
<lang 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
}</lang>
Alternative functional version:
<lang rust> fn factor(n: i32) -> Vec<i32> {
(1..=n).filter(|i| n % i == 0).collect()
} </lang>
Sather
<lang sather>class MAIN is
factors(n :INT):ARRAY{INT} is f:ARRAY{INT}; f := #; f := f.append(|1|); f := f.append(|n|); loop i ::= 2.upto!( n.flt.sqrt.int ); if n%i = 0 then f := f.append(|i|);
if (i*i) /= n then f := f.append(|n / i|); end;
end; end; f.sort; return f; end;
main is a :ARRAY{INT} := |3135, 45, 64, 53, 45, 81|; loop l ::= a.elt!; #OUT + "factors of " + l + ": "; r ::= factors(l); loop ri ::= r.elt!; #OUT + ri + " "; end; #OUT + "\n"; end; end;
end;</lang>
Scala
<lang Scala> Brute force approach:
def factors(num: Int) = { (1 to num).filter { divisor => num % divisor == 0 } }
Since factors can't be higher than sqrt(num), the code above can be edited as follows
def factors(num: Int) = { (1 to sqrt(num)).filter { divisor => num % divisor == 0 } }
</lang>
Scheme
This implementation uses a naive trial division algorithm. <lang scheme>(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)</lang>
- Output:
(1 239 4649 1111111)
Seed7
<lang 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;</lang>
- 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. <lang sequencel>Factors(num(0))[i] := i when num mod i = 0 foreach i within 1 ... num;</lang>
Slightly More Efficient Method
A slightly more efficient method, only going up to the sqrt(n). <lang sequencel>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);</lang>
Sidef
<lang ruby>func factors(n) {
gather { { |d| take(d, n//d) if d.divides(n) } << 1..n.isqrt }.sort.uniq
} for n [53, 64, 32766] {
say "factors(#{n}): #{factors(n)}"
}</lang>
- Output:
factors(53): [1, 53] factors(64): [1, 2, 4, 8, 16, 32, 64] factors(32766): [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766]
Slate
<lang slate>n@(Integer traits) primeFactors [
[| :result | result nextPut: 1. n primesDo: [| :prime | result nextPut: prime]] writingAs: {}
].</lang> where primesDo: is a part of the standard numerics library: <lang slate>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."
].</lang>
Smalltalk
Copied from the Python example, but code added to the Integer built in class:
<lang smalltalk>Integer>>factors | a | a := OrderedCollection new. 1 to: (self / 2) do: [ :i | ((self \\ i) = 0) ifTrue: [ a add: i ] ]. a add: self. ^a</lang>
Then use as follows:
<lang smalltalk> 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) </lang>
Swift
Simple implementation: <lang Swift>func factors(n: Int) -> [Int] {
return filter(1...n) { n % $0 == 0 }
}</lang> More efficient implementation: <lang Swift>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 % $0 == 0 }) { result.append(factor)
if n/factor != factor { result.append(n/factor) } } return sorted(result)
}</lang> Call: <lang Swift>println(factors(4)) println(factors(1)) println(factors(25)) println(factors(63)) println(factors(19)) println(factors(768))</lang>
- Output:
[1, 2, 4] [1] [1, 5, 25] [1, 3, 7, 9, 21, 63] [1, 19] [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768]
Tcl
<lang tcl>proc factors {n} {
set factors {} for {set i 1} {$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]</lang>
- Output:
1 2 4 8 16 32 64 1 3 5 9 15 45 1 53
UNIX Shell
This should work in all Bourne-compatible shells, assuming the system has both sort and at least one of bc or dc.
<lang>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
} </lang>
Ursa
This program takes an integer from the command line and outputs its factors. <lang ursa>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 console</lang>
Ursala
The simple way: <lang Ursala>#import std
- import nat
factors "n" = (filter not remainder/"n") nrange(1,"n")</lang>
The complicated way:
<lang Ursala>factors "n" = nleq-<&@s <.~&r,quotient>*= "n"-* (not remainder/"n")*~ nrange(1,root("n",2))</lang>
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
<lang Ursala>factors = nleq-<&@rrZPFLs+ ^(~&r,division)^*D/~& nrange/1+ &!*K31</lang>
where nleq-<&
isn't strictly necessary unless an ordered list is required.
<lang Ursala>#cast %nL
example = factors 100</lang>
- Output:
<1,2,4,5,10,20,25,50,100>
VBA
<lang vb>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</lang>
- 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"
Wortel
<lang wortel>@let {
factors1 &n !-\%%n @to n factors_tacit @(\\%% !- @to) [[ !factors1 10 !factors_tacit 100 !factors1 720 ]]
}</lang>
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] ]
XPL0
<lang XPL0>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; ]</lang>
- 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
<lang 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</lang>
- 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))
ZX Spectrum Basic
<lang zxbasic>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</lang>