Count in factors
(Redirected from Counting in Factors)
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Write a program which counts up from 1, displaying each number as the multiplication of its prime factors.
For the purpose of this task, 1 (unity) may be shown as itself.
- Example
2 is prime, so it would be shown as itself.
6 is not prime; it would be shown as .
2144 is not prime; it would be shown as .
- Related tasks
- prime decomposition
- factors of an integer
- 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
11l
F get_prime_factors(=li)
I li == 1
R ‘1’
E
V res = ‘’
V f = 2
L
I li % f == 0
res ‘’= f
li /= f
I li == 1
L.break
res ‘’= ‘ x ’
E
f++
R res
L(x) 1..17
print(‘#4: #.’.format(x, get_prime_factors(x)))
print(‘2144: ’get_prime_factors(2144))- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 10: 2 x 5 11: 11 12: 2 x 2 x 3 13: 13 14: 2 x 7 15: 3 x 5 16: 2 x 2 x 2 x 2 17: 17 2144: 2 x 2 x 2 x 2 x 2 x 67
360 Assembly
* Count in factors 24/03/2017
COUNTFAC CSECT assist plig\COUNTFAC
USING COUNTFAC,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
L R6,=F'1' i=1
DO WHILE=(C,R6,LE,=F'40') do i=1 to 40
LR R7,R6 n=i
MVI F,X'01' f=true
MVC PG,=CL80' ' clear buffer
LA R10,PG pgi=0
XDECO R6,XDEC edit i
MVC 0(12,R10),XDEC output i
LA R10,12(R10) pgi=pgi+12
MVC 0(1,R10),=C'=' output '='
LA R10,1(R10) pgi=pgi+1
IF C,R7,EQ,=F'1' THEN if n=1 then
MVI 0(R10),C'1' output n
ELSE , else
LA R8,2 p=2
DO WHILE=(CR,R8,LE,R7) do while p<=n
LR R4,R7 n
SRDA R4,32 ~
DR R4,R8 /p
IF LTR,R4,Z,R4 THEN if n//p=0 then
IF CLI,F,EQ,X'00' THEN if not f then
MVC 0(1,R10),=C'*' output '*'
LA R10,1(R10) pgi=pgi+1
ELSE , else
MVI F,X'00' f=false
ENDIF , endif
CVD R8,PP convert bin p to packed pp
MVC WORK12,MASX12 in fact L13
EDMK WORK12,PP+2 edit and mark
LA R9,WORK12+12 end of string(p)
SR R9,R1 li=lengh(p) {r1 from edmk}
MVC EDIT12,WORK12 L12<-L13
LA R4,EDIT12+12 source+12
SR R4,R9 -lengh(p)
LR R5,R9 lengh(p)
LR R2,R10 target ix
LR R3,R9 lengh(p)
MVCL R2,R4 f=f||p
AR R10,R9 ix=ix+lengh(p)
LR R4,R7 n
SRDA R4,32 ~
DR R4,R8 /p
LR R7,R5 n=n/p
ELSE , else
LA R8,1(R8) p=p+1
ENDIF , endif
ENDDO , enddo while
ENDIF , endif
XPRNT PG,L'PG print buffer
LA R6,1(R6) i++
ENDDO , enddo i
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
F DS X flag first factor
DS 0D alignment for cvd
PP DS PL8 packed CL8
EDIT12 DS CL12 target CL12
WORK12 DS CL13 char CL13
MASX12 DC X'40',9X'20',X'212060' CL13
XDEC DS CL12 temp
PG DS CL80 buffer
YREGS
END COUNTFAC- 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
19=19
20=2*2*5
21=3*7
22=2*11
23=23
24=2*2*2*3
25=5*5
26=2*13
27=3*3*3
28=2*2*7
29=29
30=2*3*5
31=31
32=2*2*2*2*2
33=3*11
34=2*17
35=5*7
36=2*2*3*3
37=37
38=2*19
39=3*13
40=2*2*2*5
Action!
PROC PrintFactors(CARD a)
BYTE notFirst
CARD p
IF a=1 THEN
PrintC(a) RETURN
FI
p=2 notFirst=0
WHILE p<=a
DO
IF a MOD p=0 THEN
IF notFirst THEN
Put('x)
FI
notFirst=1
PrintC(p)
a==/p
ELSE
p==+1
FI
OD
RETURN
PROC Main()
CARD i
FOR i=1 TO 1000
DO
PrintC(i) Put('=)
PrintFactors(i)
PutE()
OD
RETURN- Output:
Screenshot from Atari 8-bit computer
1=1 2=2 3=3 4=2x2 5=5 ... 995=5x199 996=2x2x3x83 997=997 998=2x499 999=3x3x3x37 1000=2x2x2x5x5x5
Ada
The solution uses the generic package Prime_Numbers from Prime decomposition#Ada
- count.adb
with Ada.Command_Line, Ada.Text_IO, Prime_Numbers;
procedure Count is
package Prime_Nums is new Prime_Numbers
(Number => Natural, Zero => 0, One => 1, Two => 2); use Prime_Nums;
procedure Put (List : Number_List) is
begin
for Index in List'Range loop
Ada.Text_IO.Put (Integer'Image (List (Index)));
if Index /= List'Last then
Ada.Text_IO.Put (" x");
end if;
end loop;
end Put;
N : Natural := 1;
Max_N : Natural := 15; -- the default for Max_N
begin
if Ada.Command_Line.Argument_Count = 1 then -- read Max_N from command line
Max_N := Integer'Value (Ada.Command_Line.Argument (1));
end if; -- else use the default
loop
Ada.Text_IO.Put (Integer'Image (N) & ": ");
Put (Decompose (N));
Ada.Text_IO.New_Line;
N := N + 1;
exit when N > Max_N;
end loop;
end Count;
- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 10: 2 x 5 11: 11 12: 2 x 2 x 3 13: 13 14: 2 x 7 15: 3 x 5
ALGOL 68
OP +:= = (REF FLEX []INT a, INT b) VOID:
BEGIN
[UPB a + 1] INT c;
c[:UPB a] := a;
c[UPB a+1:] := b;
a := c
END;
PROC factorize = (INT nn) []INT:
BEGIN
IF nn = 1 THEN (1)
ELSE
INT k := 2, n := nn;
FLEX[0]INT result;
WHILE n > 1 DO
WHILE n MOD k = 0 DO
result +:= k;
n := n % k
OD;
k +:= 1
OD;
result
FI
END;
FLEX[0]INT factors;
FOR i TO 22 DO
factors := factorize (i);
print ((whole (i, 0), " = "));
FOR j TO UPB factors DO
(j /= 1 | print (" × "));
print ((whole (factors[j], 0)))
OD;
print ((new line))
OD- 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 19 = 19 20 = 2 × 2 × 5 21 = 3 × 7 22 = 2 × 11
ALGOL W
begin % show numbers and their prime factors %
% shows nand its prime factors %
procedure showFactors ( integer value n ) ;
if n <= 3 then write( i_w := 1, s_w := 0, n, ": ", n )
else begin
integer v, f; logical first;
first := true;
v := n;
write( i_w := 1, s_w := 0, n, ": " );
while not odd( v ) and v > 1 do begin
if not first then writeon( s_w := 0, " x " );
writeon( i_w := 1, s_w := 0, 2 );
v := v div 2;
first := false
end while_not_odd_v ;
f := 1;
while v > 1 do begin
f := f + 2;
while v rem f = 0 do begin
if not first then writeon( s_w := 0, " x " );
writeon( i_w := 1, s_w := 0, f );
v := v div f;
first := false
end while_v_rem_f_eq_0
end while_v_gt_0_and_f_le_v
end showFactors ;
% show the factors of various ranges - same as Wren %
for i := 1 until 9 do showFactors( i );
write( "... " );
for i := 2144 until 2154 do showFactors( i );
write( "... " );
for i := 9987 until 9999 do showFactors( i )
end.- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 ... 2144: 2 x 2 x 2 x 2 x 2 x 67 2145: 3 x 5 x 11 x 13 2146: 2 x 29 x 37 2147: 19 x 113 2148: 2 x 2 x 3 x 179 2149: 7 x 307 2150: 2 x 5 x 5 x 43 2151: 3 x 3 x 239 2152: 2 x 2 x 2 x 269 2153: 2153 2154: 2 x 3 x 359 ... 9987: 3 x 3329 9988: 2 x 2 x 11 x 227 9989: 7 x 1427 9990: 2 x 3 x 3 x 3 x 5 x 37 9991: 97 x 103 9992: 2 x 2 x 2 x 1249 9993: 3 x 3331 9994: 2 x 19 x 263 9995: 5 x 1999 9996: 2 x 2 x 3 x 7 x 7 x 17 9997: 13 x 769 9998: 2 x 4999 9999: 3 x 3 x 11 x 101
ARM Assembly
/* ARM assembly Raspberry PI */
/* program countFactors.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes */
/************************************/
.include "../constantes.inc"
.equ NBFACT, 33
.equ MAXI, 1<<31
//.equ NOMBRE, 65537
//.equ NOMBRE, 99999999
.equ NOMBRE, 2144
//.equ NOMBRE, 529
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessNumber: .asciz "Number @ : "
szMessResultFact: .asciz "@ "
szCarriageReturn: .asciz "\n"
szErrorGen: .asciz "Program error !!!\n"
szMessPrime: .asciz "This number is prime.\n"
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
tbZoneDecom: .skip 8 * NBFACT // factor 4 bytes, number of each factor 4 bytes
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
ldr r7,iNombre @ number
mov r0,r7
ldr r1,iAdrsZoneConv
bl conversion10 @ call décimal conversion
ldr r0,iAdrszMessNumber
ldr r1,iAdrsZoneConv @ insert conversion in message
bl strInsertAtCharInc
bl affichageMess @ display message
mov r0,r7
ldr r1,iAdrtbZoneDecom
bl decompFact
cmp r0,#-1
beq 98f @ error ?
mov r1,r0
ldr r0,iAdrtbZoneDecom
bl displayDivisors
b 100f
98:
ldr r0,iAdrszErrorGen
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrszCarriageReturn: .int szCarriageReturn
iAdrszMessResultFact: .int szMessResultFact
iAdrszErrorGen: .int szErrorGen
iAdrsZoneConv: .int sZoneConv
iAdrtbZoneDecom: .int tbZoneDecom
iAdrszMessNumber: .int szMessNumber
iNombre: .int NOMBRE
/******************************************************************/
/* display divisors function */
/******************************************************************/
/* r0 contains address of divisors area */
/* r1 contains the number of area items */
displayDivisors:
push {r2-r8,lr} @ save registers
cmp r1,#0
beq 100f
mov r2,r1
mov r3,#0 @ indice
mov r4,r0
1:
add r5,r4,r3,lsl #3
ldr r7,[r5] @ load factor
ldr r6,[r5,#4] @ load number of factor
mov r8,#0 @ display factor counter
2:
mov r0,r7
ldr r1,iAdrsZoneConv
bl conversion10 @ call décimal conversion
ldr r0,iAdrszMessResultFact
ldr r1,iAdrsZoneConv @ insert conversion in message
bl strInsertAtCharInc
bl affichageMess @ display message
add r8,#1 @ increment counter
cmp r8,r6 @ same factors number ?
blt 2b
add r3,#1 @ other ithem
cmp r3,r2 @ items maxi ?
blt 1b
ldr r0,iAdrszCarriageReturn
bl affichageMess
b 100f
100:
pop {r2-r8,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* factor decomposition */
/******************************************************************/
/* r0 contains number */
/* r1 contains address of divisors area */
/* r0 return divisors items in table */
decompFact:
push {r1-r8,lr} @ save registers
mov r5,r1
mov r8,r0 @ save number
bl isPrime @ prime ?
cmp r0,#1
beq 98f @ yes is prime
mov r4,#0 @ raz indice
mov r1,#2 @ first divisor
mov r6,#0 @ previous divisor
mov r7,#0 @ number of same divisors
2:
mov r0,r8 @ dividende
bl division @ r1 divisor r2 quotient r3 remainder
cmp r3,#0
bne 5f @ if remainder <> zero -> no divisor
mov r8,r2 @ else quotient -> new dividende
cmp r1,r6 @ same divisor ?
beq 4f @ yes
cmp r6,#0 @ no but is the first divisor ?
beq 3f @ yes
str r6,[r5,r4,lsl #2] @ else store in the table
add r4,r4,#1 @ and increment counter
str r7,[r5,r4,lsl #2] @ store counter
add r4,r4,#1 @ next item
mov r7,#0 @ and raz counter
3:
mov r6,r1 @ new divisor
4:
add r7,r7,#1 @ increment counter
b 7f @ and loop
/* not divisor -> increment next divisor */
5:
cmp r1,#2 @ if divisor = 2 -> add 1
addeq r1,#1
addne r1,#2 @ else add 2
b 2b
/* divisor -> test if new dividende is prime */
7:
mov r3,r1 @ save divisor
cmp r8,#1 @ dividende = 1 ? -> end
beq 10f
mov r0,r8 @ new dividende is prime ?
mov r1,#0
bl isPrime @ the new dividende is prime ?
cmp r0,#1
bne 10f @ the new dividende is not prime
cmp r8,r6 @ else dividende is same divisor ?
beq 9f @ yes
cmp r6,#0 @ no but is the first divisor ?
beq 8f @ yes it is a first
str r6,[r5,r4,lsl #2] @ else store in table
add r4,r4,#1 @ and increment counter
str r7,[r5,r4,lsl #2] @ and store counter
add r4,r4,#1 @ next item
8:
mov r6,r8 @ new dividende -> divisor prec
mov r7,#0 @ and raz counter
9:
add r7,r7,#1 @ increment counter
b 11f
10:
mov r1,r3 @ current divisor = new divisor
cmp r1,r8 @ current divisor > new dividende ?
ble 2b @ no -> loop
/* end decomposition */
11:
str r6,[r5,r4,lsl #2] @ store last divisor
add r4,r4,#1
str r7,[r5,r4,lsl #2] @ and store last number of same divisors
add r4,r4,#1
lsr r0,r4,#1 @ return number of table items
mov r3,#0
str r3,[r5,r4,lsl #2] @ store zéro in last table item
add r4,r4,#1
str r3,[r5,r4,lsl #2] @ and zero in counter same divisor
b 100f
98:
ldr r0,iAdrszMessPrime
bl affichageMess
mov r0,#1 @ return code
b 100f
99:
ldr r0,iAdrszErrorGen
bl affichageMess
mov r0,#-1 @ error code
b 100f
100:
pop {r1-r8,lr} @ restaur registers
bx lr
iAdrszMessPrime: .int szMessPrime
/***************************************************/
/* check if a number is prime */
/***************************************************/
/* r0 contains the number */
/* r0 return 1 if prime 0 else */
@2147483647
@4294967297
@131071
isPrime:
push {r1-r6,lr} @ save registers
cmp r0,#0
beq 90f
cmp r0,#17
bhi 1f
cmp r0,#3
bls 80f @ for 1,2,3 return prime
cmp r0,#5
beq 80f @ for 5 return prime
cmp r0,#7
beq 80f @ for 7 return prime
cmp r0,#11
beq 80f @ for 11 return prime
cmp r0,#13
beq 80f @ for 13 return prime
cmp r0,#17
beq 80f @ for 17 return prime
1:
tst r0,#1 @ even ?
beq 90f @ yes -> not prime
mov r2,r0 @ save number
sub r1,r0,#1 @ exposant n - 1
mov r0,#3 @ base
bl moduloPuR32 @ compute base power n - 1 modulo n
cmp r0,#1
bne 90f @ if <> 1 -> not prime
mov r0,#5
bl moduloPuR32
cmp r0,#1
bne 90f
mov r0,#7
bl moduloPuR32
cmp r0,#1
bne 90f
mov r0,#11
bl moduloPuR32
cmp r0,#1
bne 90f
mov r0,#13
bl moduloPuR32
cmp r0,#1
bne 90f
mov r0,#17
bl moduloPuR32
cmp r0,#1
bne 90f
80:
mov r0,#1 @ is prime
b 100f
90:
mov r0,#0 @ no prime
100: @ fin standard de la fonction
pop {r1-r6,lr} @ restaur des registres
bx lr @ retour de la fonction en utilisant lr
/********************************************************/
/* Calcul modulo de b puissance e modulo m */
/* Exemple 4 puissance 13 modulo 497 = 445 */
/* */
/********************************************************/
/* r0 nombre */
/* r1 exposant */
/* r2 modulo */
/* r0 return result */
moduloPuR32:
push {r1-r7,lr} @ save registers
cmp r0,#0 @ verif <> zero
beq 100f
cmp r2,#0 @ verif <> zero
beq 100f @
1:
mov r4,r2 @ save modulo
mov r5,r1 @ save exposant
mov r6,r0 @ save base
mov r3,#1 @ start result
mov r1,#0 @ division de r0,r1 par r2
bl division32R
mov r6,r2 @ base <- remainder
2:
tst r5,#1 @ exposant even or odd
beq 3f
umull r0,r1,r6,r3
mov r2,r4
bl division32R
mov r3,r2 @ result <- remainder
3:
umull r0,r1,r6,r6
mov r2,r4
bl division32R
mov r6,r2 @ base <- remainder
lsr r5,#1 @ left shift 1 bit
cmp r5,#0 @ end ?
bne 2b
mov r0,r3
100: @ fin standard de la fonction
pop {r1-r7,lr} @ restaur des registres
bx lr @ retour de la fonction en utilisant lr
/***************************************************/
/* division number 64 bits in 2 registers by number 32 bits */
/***************************************************/
/* r0 contains lower part dividende */
/* r1 contains upper part dividende */
/* r2 contains divisor */
/* r0 return lower part quotient */
/* r1 return upper part quotient */
/* r2 return remainder */
division32R:
push {r3-r9,lr} @ save registers
mov r6,#0 @ init upper upper part remainder !!
mov r7,r1 @ init upper part remainder with upper part dividende
mov r8,r0 @ init lower part remainder with lower part dividende
mov r9,#0 @ upper part quotient
mov r4,#0 @ lower part quotient
mov r5,#32 @ bits number
1: @ begin loop
lsl r6,#1 @ shift upper upper part remainder
lsls r7,#1 @ shift upper part remainder
orrcs r6,#1
lsls r8,#1 @ shift lower part remainder
orrcs r7,#1
lsls r4,#1 @ shift lower part quotient
lsl r9,#1 @ shift upper part quotient
orrcs r9,#1
@ divisor sustract upper part remainder
subs r7,r2
sbcs r6,#0 @ and substract carry
bmi 2f @ négative ?
@ positive or equal
orr r4,#1 @ 1 -> right bit quotient
b 3f
2: @ negative
orr r4,#0 @ 0 -> right bit quotient
adds r7,r2 @ and restaur remainder
adc r6,#0
3:
subs r5,#1 @ decrement bit size
bgt 1b @ end ?
mov r0,r4 @ lower part quotient
mov r1,r9 @ upper part quotient
mov r2,r7 @ remainder
100: @ function end
pop {r3-r9,lr} @ restaur registers
bx lr
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"Number 2144 : 2 2 2 2 2 67
Arturo
loop 1..30 'x [
fs: [1]
if x<>1 -> fs: factors.prime x
print [pad to :string x 3 "=" join.with:" x " to [:string] fs]
]
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5 21 = 3 x 7 22 = 2 x 11 23 = 23 24 = 2 x 2 x 2 x 3 25 = 5 x 5 26 = 2 x 13 27 = 3 x 3 x 3 28 = 2 x 2 x 7 29 = 29 30 = 2 x 3 x 5
AutoHotkey
factorize(n){
if n = 1
return 1
if n < 1
return false
result := 0, m := n, k := 2
While n >= k{
while !Mod(m, k){
result .= " * " . k, m /= k
}
k++
}
return SubStr(result, 5)
}
Loop 22
out .= A_Index ": " factorize(A_index) "`n"
MsgBox % out
- 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 19: 19 20: 2 * 2 * 5 21: 3 * 7 22: 2 * 11
AWK
# syntax: GAWK -f COUNT_IN_FACTORS.AWK
BEGIN {
fmt = "%d=%s\n"
for (i=1; i<=16; i++) {
printf(fmt,i,factors(i))
}
i = 2144; printf(fmt,i,factors(i))
i = 6358; printf(fmt,i,factors(i))
exit(0)
}
function factors(n, f,p) {
if (n == 1) {
return(1)
}
p = 2
while (p <= n) {
if (n % p == 0) {
f = sprintf("%s%s*",f,p)
n /= p
}
else {
p++
}
}
return(substr(f,1,length(f)-1))
}
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 2144=2*2*2*2*2*67 6358=2*11*17*17
BASIC
Applesoft BASIC
100 FOR I = 1 TO 20
110 GOSUB 200"FACTORIAL
120 PRINT I" = "FA$
130 NEXT I
140 END
200 FA$ = "1"
210 LET NUM = I
220 LET O = 5 - (I = 1) * 4
230 FOR F = 2 TO I
240 LET M = INT (NUM / F) * F
250 IF NUM - M GOTO 300
260 LET NUM = NUM / F
270 LET F$ = STR $(F)
280 FA$ = FA$ + " X " + F$
290 LET F = F - 1
300 NEXT F
310 FA$ = MID$ (FA$,O)
320 RETURNBASIC256
for i = 1 to 20
print i; " = "; factorial$(i)
next i
end
function factorial$ (num)
factor$ = "" : x$ = ""
if num = 1 then return "1"
fct = 2
while fct <= num
if (num mod fct) = 0 then
factor$ += x$ + string(fct)
x$ = " x "
num /= fct
else
fct += 1
end if
end while
return factor$
end function
Chipmunk Basic
100 cls
110 for i = 1 to 20
120 rem for i = 1000 to 1016
130 print i;"= ";factorial$(i)
140 next i
150 end
160 function factorial$(num)
170 factor$ = "" : x$ = ""
180 if num = 1 then print "1"
190 fct = 2
200 while fct <= num
210 if (num mod fct) = 0 then
220 factor$ = factor$+x$+str$(fct)
230 x$ = " x "
240 num = num/fct
250 else
260 fct = fct+1
270 endif
280 wend
290 print factor$
300 end function
True BASIC
FUNCTION factorial$ (num)
LET f$ = ""
LET x$ = ""
IF num = 1 THEN LET f$ = "1"
LET fct = 2
DO WHILE fct <= num
IF MOD(num, fct) = 0 THEN
LET f$ = f$ & x$ & STR$(fct)
LET x$ = " x "
LET num = num / fct
ELSE
LET fct = fct + 1
END IF
LOOP
LET factorial$ = f$
END FUNCTION
FOR i = 1 TO 20
PRINT i; "= "; factorial$(i)
NEXT i
END
Yabasic
for i = 1 to 20
print i, " = ", factorial$(i)
next i
end
sub factorial$ (num)
local f$, x$
f$ = "" : x$ = ""
if num = 1 return "1"
fct = 2
while fct <= num
if mod(num, fct) = 0 then
f$ = f$ + x$ + str$(fct)
x$ = " x "
num = num / fct
else
fct = fct + 1
end if
wend
return f$
end sub
BBC BASIC
FOR i% = 1 TO 20
PRINT i% " = " FNfactors(i%)
NEXT
END
DEF FNfactors(N%)
LOCAL P%, f$
IF N% = 1 THEN = "1"
P% = 2
WHILE P% <= N%
IF (N% MOD P%) = 0 THEN
f$ += STR$(P%) + " x "
N% DIV= P%
ELSE
P% += 1
ENDIF
ENDWHILE
= LEFT$(f$, LEN(f$) - 3)
Output:
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17 = 17
18 = 2 x 3 x 3
19 = 19
20 = 2 x 2 x 5
Befunge
Lists the first 100 entries in the sequence. If you wish to extend that, the upper limit is implementation dependent, but may be as low as 130 for an interpreter with signed 8 bit data cells (131 is the first prime outside that range).
1>>>>:.48*"=",,::1-#v_.v
$<<<^_@#-"e":+1,+55$2<<<
v4_^#-1:/.:g00_00g1+>>0v
>8*"x",,:00g%!^!%g00:p0<
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 . . .
C
Code includes a dynamically extending prime number list. The program doesn't stop until you kill it, or it runs out of memory, or it overflows.
#include <stdio.h>
#include <stdlib.h>
typedef unsigned long long ULONG;
ULONG get_prime(int idx)
{
static long n_primes = 0, alloc = 0;
static ULONG *primes = 0;
ULONG last, p;
int i;
if (idx >= n_primes) {
if (n_primes >= alloc) {
alloc += 16; /* be conservative */
primes = realloc(primes, sizeof(ULONG) * alloc);
}
if (!n_primes) {
primes[0] = 2;
primes[1] = 3;
n_primes = 2;
}
last = primes[n_primes-1];
while (idx >= n_primes) {
last += 2;
for (i = 0; i < n_primes; i++) {
p = primes[i];
if (p * p > last) {
primes[n_primes++] = last;
break;
}
if (last % p == 0) break;
}
}
}
return primes[idx];
}
int main()
{
ULONG n, x, p;
int i, first;
for (x = 1; ; x++) {
printf("%lld = ", n = x);
for (i = 0, first = 1; ; i++) {
p = get_prime(i);
while (n % p == 0) {
n /= p;
if (!first) printf(" x ");
first = 0;
printf("%lld", p);
}
if (n <= p * p) break;
}
if (first) printf("%lld\n", n);
else if (n > 1) printf(" x %lld\n", n);
else printf("\n");
}
return 0;
}
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 . . .
C#
using System;
using System.Collections.Generic;
namespace prog
{
class MainClass
{
public static void Main (string[] args)
{
for( int i=1; i<=22; i++ )
{
List<int> f = Factorize(i);
Console.Write( i + ": " + f[0] );
for( int j=1; j<f.Count; j++ )
{
Console.Write( " * " + f[j] );
}
Console.WriteLine();
}
}
public static List<int> Factorize( int n )
{
List<int> l = new List<int>();
if ( n == 1 )
{
l.Add(1);
}
else
{
int k = 2;
while( n > 1 )
{
while( n % k == 0 )
{
l.Add( k );
n /= k;
}
k++;
}
}
return l;
}
}
}
C++
#include <iostream>
#include <iomanip>
using namespace std;
void getPrimeFactors( int li )
{
int f = 2; string res;
if ( li == 1 ) res = "1";
else
{
while ( true )
{
if( !( li % f ) )
{
res += to_string(f);
li /= f; if( li == 1 ) break;
res += " x ";
}
else f++;
}
}
cout << res << "\n";
}
int main( int argc, char* argv[] )
{
for ( int x = 1; x < 101; x++ )
{
cout << right << setw( 4 ) << x << ": ";
getPrimeFactors( x );
}
cout << 2144 << ": "; getPrimeFactors( 2144 );
cout << "\n\n";
return system( "pause" );
}
- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 10: 2 x 5 11: 11 12: 2 x 2 x 3 13: 13 14: 2 x 7 15: 3 x 5 16: 2 x 2 x 2 x 2 17: 17 18: 2 x 3 x 3 19: 19 20: 2 x 2 x 5 21: 3 x 7 22: 2 x 11 23: 23 24: 2 x 2 x 2 x 3 . . .
Clojure
(ns listfactors
(:gen-class))
(defn factors
"Return a list of factors of N."
([n]
(factors n 2 ()))
([n k acc]
(cond
(= n 1) (if (empty? acc)
[n]
(sort acc))
(>= k n) (if (empty? acc)
[n]
(sort (cons n acc)))
(= 0 (rem n k)) (recur (quot n k) k (cons k acc))
:else (recur n (inc k) acc))))
(doseq [q (range 1 26)]
(println q " = " (clojure.string/join " x "(factors q))))
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5 21 = 3 x 7 22 = 2 x 11 23 = 23 24 = 2 x 2 x 2 x 3 25 = 5 x 5
CoffeeScript
count_primes = (max) ->
# Count through the natural numbers and give their prime
# factorization. This algorithm uses no division.
# Instead, each prime number starts a rolling odometer
# to help subsequent factorizations. The algorithm works similar
# to the Sieve of Eratosthenes, as we note when each prime number's
# odometer rolls a digit. (As it turns out, as long as your computer
# is not horribly slow at division, you're better off just doing simple
# prime factorizations on each new n vs. using this algorithm.)
console.log "1 = 1"
primes = []
n = 2
while n <= max
factors = []
for prime_odometer in primes
# digits are an array w/least significant digit in
# position 0; for example, [3, [0]] will roll as
# follows:
# [0] -> [1] -> [2] -> [0, 1]
[base, digits] = prime_odometer
i = 0
while true
digits[i] += 1
break if digits[i] < base
digits[i] = 0
factors.push base
i += 1
if i >= digits.length
digits.push 0
if factors.length == 0
primes.push [n, [0, 1]]
factors.push n
console.log "#{n} = #{factors.join('*')}"
n += 1
primes.length
num_primes = count_primes 10000
console.log num_primes
Common Lisp
Auto extending prime list:
(defparameter *primes*
(make-array 10 :adjustable t :fill-pointer 0 :element-type 'integer))
(mapc #'(lambda (x) (vector-push x *primes*)) '(2 3 5 7))
(defun extend-primes (n)
(let ((p (+ 2 (elt *primes* (1- (length *primes*))))))
(loop for i = p then (+ 2 i)
while (<= (* i i) n) do
(if (primep i t) (vector-push-extend i *primes*)))))
(defun primep (n &optional skip)
(if (not skip) (extend-primes n))
(if (= n 1) nil
(loop for p across *primes* while (<= (* p p) n)
never (zerop (mod n p)))))
(defun factors (n)
(extend-primes n)
(loop with res for x across *primes* while (> n (* x x)) do
(loop while (zerop (rem n x)) do
(setf n (/ n x))
(push x res))
finally (return (if (> n 1) (cons n res) res))))
(loop for n from 1 do
(format t "~a: ~{~a~^ × ~}~%" n (reverse (factors n))))
- Output:
1: 2: 2 3: 3 4: 4 5: 5 6: 2 × 3 7: 7 8: 2 × 2 × 2 9: 9 10: 2 × 5 11: 11 12: 2 × 2 × 3 13: 13 14: 2 × 7 ...
Without saving the primes, and not all that much slower (probably because above code was not well-written):
(defun factors (n)
(loop with res for x from 2 to (isqrt n) do
(loop while (zerop (rem n x)) do
(setf n (/ n x))
(push x res))
finally (return (if (> n 1) (cons n res) res))))
(loop for n from 1 do
(format t "~a: ~{~a~^ × ~}~%" n (reverse (factors n))))
D
int[] factorize(in int n) pure nothrow
in {
assert(n > 0);
} body {
if (n == 1) return [1];
int[] result;
int m = n, k = 2;
while (n >= k) {
while (m % k == 0) {
result ~= k;
m /= k;
}
k++;
}
return result;
}
void main() {
import std.stdio;
foreach (i; 1 .. 22)
writefln("%d: %(%d × %)", i, i.factorize());
}
- 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 19: 19 20: 2 × 2 × 5 21: 3 × 7
Alternative Version
Library uiprimes is a homebrew library to generate prime numbers upto the maximum 32bit unsigned integer range 2^32-1, by using a pre-generated bit array of Sieve of Eratosthenes (a dll in size of ~256M bytes :p ).
import std.stdio, std.math, std.conv, std.algorithm,
std.array, std.string, import xt.uiprimes;
pragma(lib, "uiprimes.lib");
// function _factorize_ included in uiprimes.lib
ulong[] factorize(ulong n) {
if (n == 0) return [];
if (n == 1) return [1];
ulong[] res;
uint limit = cast(uint)(1 + sqrt(n));
foreach (p; Primes(limit)) {
if (n == 1) break;
if (0UL == (n % p))
while((n > 1) && (0UL == (n % p ))) {
res ~= p;
n /= p;
}
}
if (n > 1)
res ~= [n];
return res;
}
string productStr(T)(in T[] nums) {
return nums.map!text().join(" x ");
}
void main() {
foreach (i; 1 .. 21)
writefln("%2d = %s", i, productStr(factorize(i)));
}
DCL
Assumes file primes.txt is a list of prime numbers;
$ close /nolog primes
$ on control_y then $ goto clean
$
$ n = 1
$ outer_loop:
$ x = n
$ open primes primes.txt
$
$ loop1:
$ read /end_of_file = prime primes prime
$ prime = f$integer( prime )
$ loop2:
$ t = x / prime
$ if t * prime .eq. x
$ then
$ if f$type( factorization ) .eqs. ""
$ then
$ factorization = f$string( prime )
$ else
$ factorization = factorization + "*" + f$string( prime )
$ endif
$ if t .eq. 1 then $ goto done
$ x = t
$ goto loop2
$ else
$ goto loop1
$ endif
$ prime:
$ if f$type( factorization ) .eqs. ""
$ then
$ factorization = f$string( x )
$ else
$ factorization = factorization + "*" + f$string( x )
$ endif
$ done:
$ write sys$output f$fao( "!4SL = ", n ), factorization
$ delete /symbol factorization
$ close primes
$ n = n + 1
$ if n .le. 2144 then $ goto outer_loop
$ exit
$
$ clean:
$ close /nolog primes
- Output:
$ @count_in_factors 1 = 1 2 = 2 3 = 3 4 = 2*2 5 = 5 6 = 2*3 ... 2144 = 2*2*2*2*2*67
Delphi
See Pascal.
DWScript
function Factorize(n : Integer) : String;
begin
if n <= 1 then
Exit('1');
var k := 2;
while n >= k do begin
while (n mod k) = 0 do begin
Result += ' * '+IntToStr(k);
n := n div k;
end;
Inc(k);
end;
Result:=SubStr(Result, 4);
end;
var i : Integer;
for i := 1 to 22 do
PrintLn(IntToStr(i) + ': ' + Factorize(i));
- 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 19: 19 20: 2 * 2 * 5 21: 3 * 7 22: 2 * 11
EasyLang
proc decompose num . primes[] .
primes[] = [ ]
t = 2
while t * t <= num
if num mod t = 0
primes[] &= t
num = num / t
else
t += 1
.
.
primes[] &= num
.
for i = 1 to 30
write i & ": "
decompose i primes[]
for j = 1 to len primes[]
if j > 1
write " x "
.
write primes[j]
.
print ""
primes[] = [ ]
.- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 10: 2 x 5 11: 11 12: 2 x 2 x 3 13: 13 14: 2 x 7 15: 3 x 5 16: 2 x 2 x 2 x 2 17: 17 18: 2 x 3 x 3 19: 19 20: 2 x 2 x 5 21: 3 x 7 22: 2 x 11 23: 23 24: 2 x 2 x 2 x 3 25: 5 x 5 26: 2 x 13 27: 3 x 3 x 3 28: 2 x 2 x 7 29: 29 30: 2 x 3 x 5
EchoLisp
(define (task (nfrom 2) (range 20))
(for ((i (in-range nfrom (+ nfrom range))))
(writeln i "=" (string-join (prime-factors i) " x "))))
- Output:
(task 1_000_000_000) 1000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 1000000001 = 7 x 11 x 13 x 19 x 52579 1000000002 = 2 x 3 x 43 x 983 x 3943 1000000003 = 23 x 307 x 141623 1000000004 = 2 x 2 x 41 x 41 x 148721 1000000005 = 3 x 5 x 66666667 1000000006 = 2 x 500000003 1000000007 = 1000000007 1000000008 = 2 x 2 x 2 x 3 x 3 x 7 x 109 x 109 x 167 1000000009 = 1000000009 1000000010 = 2 x 5 x 17 x 5882353 1000000011 = 3 x 29 x 11494253 1000000012 = 2 x 2 x 11 x 47 x 79 x 6121 1000000013 = 7699 x 129887 1000000014 = 2 x 3 x 13 x 103 x 124471 1000000015 = 5 x 7 x 31 x 223 x 4133 1000000016 = 2 x 2 x 2 x 2 x 62500001 1000000017 = 3 x 3 x 111111113 1000000018 = 2 x 500000009 1000000019 = 83 x 12048193
Eiffel
class
COUNT_IN_FACTORS
feature
display_factor (p: INTEGER)
-- Factors of all integers up to 'p'.
require
p_positive: p > 0
local
factors: ARRAY [INTEGER]
do
across
1 |..| p as c
loop
io.new_line
io.put_string (c.item.out + "%T")
factors := factor (c.item)
across
factors as f
loop
io.put_integer (f.item)
if f.is_last = False then
io.put_string (" x ")
end
end
end
end
factor (p: INTEGER): ARRAY [INTEGER]
-- Prime decomposition of 'p'.
require
p_positive: p > 0
local
div, i, next, rest: INTEGER
do
create Result.make_empty
if p = 1 then
Result.force (1, 1)
end
div := 2
next := 3
rest := p
from
i := 1
until
rest = 1
loop
from
until
rest \\ div /= 0
loop
Result.force (div, i)
rest := (rest / div).floor
i := i + 1
end
div := next
next := next + 2
end
ensure
is_divisor: across Result as r all p \\ r.item = 0 end
end
end
Test Output:
1 1 2 2 3 3 4 2 x 2 5 5 6 2 x 3 7 7 8 2 x 2 x 2 9 3 x 3 10 2 x 5 ... 4990 2 x 5 x 499 4991 7 x 23 x 31 4992 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 4993 4993 4994 2 x 11 x 227 4995 3 x 3 x 3 x 5 x 37 4996 2 x 2 x 1249 4997 19 x 263 4998 2 x 3 x 7 x 7 x 17 4999 4999 5000 2 x 2 x 2 x 5 x 5 x 5 x 5
Elixir
defmodule RC do
def factor(n), do: factor(n, 2, [])
def factor(n, i, fact) when n < i*i, do: Enum.reverse([n|fact])
def factor(n, i, fact) do
if rem(n,i)==0, do: factor(div(n,i), i, [i|fact]),
else: factor(n, i+1, fact)
end
end
Enum.each(1..20, fn n ->
IO.puts "#{n}: #{Enum.join(RC.factor(n)," x ")}" end)
- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 10: 2 x 5 11: 11 12: 2 x 2 x 3 13: 13 14: 2 x 7 15: 3 x 5 16: 2 x 2 x 2 x 2 17: 17 18: 2 x 3 x 3 19: 19 20: 2 x 2 x 5
Euphoria
function factorize(integer n)
sequence result
integer k
if n = 1 then
return {1}
else
k = 2
result = {}
while n > 1 do
while remainder(n, k) = 0 do
result &= k
n /= k
end while
k += 1
end while
return result
end if
end function
sequence factors
for i = 1 to 22 do
printf(1, "%d: ", i)
factors = factorize(i)
for j = 1 to length(factors)-1 do
printf(1, "%d * ", factors[j])
end for
printf(1, "%d\n", factors[$])
end for- 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 19: 19 20: 2 * 2 * 5 21: 3 * 7 22: 2 * 11
F#
let factorsOf (num) =
Seq.unfold (fun (f, n) ->
let rec genFactor (f, n) =
if f > n then None
elif n % f = 0 then Some (f, (f, n/f))
else genFactor (f+1, n)
genFactor (f, n)) (2, num)
let showLines = Seq.concat (seq { yield seq{ yield(Seq.singleton 1)}; yield (Seq.skip 2 (Seq.initInfinite factorsOf))})
showLines |> Seq.iteri (fun i f -> printfn "%d = %s" (i+1) (String.Join(" * ", Seq.toArray f)))
- 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 : 2140 = 2 * 2 * 5 * 107 2141 = 2141 2142 = 2 * 3 * 3 * 7 * 17 2143 = 2143 2144 = 2 * 2 * 2 * 2 * 2 * 67 2145 = 3 * 5 * 11 * 13 2146 = 2 * 29 * 37 2147 = 19 * 113 :
Factor
USING: io kernel math.primes.factors math.ranges prettyprint
sequences ;
: .factors ( n -- )
dup pprint ": " write factors
[ " × " write ] [ pprint ] interleave nl ;
"1: 1" print 2 20 [a,b] [ .factors ] each
- 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 19: 19 20: 2 × 2 × 5
Forth
: .factors ( n -- )
2
begin 2dup dup * >=
while 2dup /mod swap
if drop 1+ 1 or \ next odd number
else -rot nip dup . ." x "
then
repeat
drop . ;
: main ( n -- )
." 1 : 1" cr
1+ 2 ?do i . ." : " i .factors cr loop ;
15 main bye
Fortran
Please find the example output along with the build instructions in the comments at the start of the FORTRAN 2008 source. Compiler: gfortran from the GNU compiler collection. Command interpreter: bash. The code writes j assertions which don't prove primality of the factors but does prove they are the factors.
This algorithm creates a sieve of Eratosthenes, storing the largest prime factor to mark composites. It then finds prime factors by repeatedly looking up the value in the sieve, then dividing by the factor found until the value is itself prime. Using the sieve table to store factors rather than as a plain bitmap was to me a novel idea.
!-*- mode: compilation; default-directory: "/tmp/" -*-
!Compilation started at Thu Jun 6 23:29:06
!
!a=./f && make $a && echo -2 | OMP_NUM_THREADS=2 $a
!gfortran -std=f2008 -Wall -fopenmp -ffree-form -fall-intrinsics -fimplicit-none f.f08 -o f
! assert 1 = */ 1
! assert 2 = */ 2
! assert 3 = */ 3
! assert 4 = */ 2 2
! assert 5 = */ 5
! assert 6 = */ 2 3
! assert 7 = */ 7
! assert 8 = */ 2 2 2
! assert 9 = */ 3 3
! assert 10 = */ 2 5
! assert 11 = */ 11
! assert 12 = */ 3 2 2
! assert 13 = */ 13
! assert 14 = */ 2 7
! assert 15 = */ 3 5
! assert 16 = */ 2 2 2 2
! assert 17 = */ 17
! assert 18 = */ 3 2 3
! assert 19 = */ 19
! assert 20 = */ 2 2 5
! assert 21 = */ 3 7
! assert 22 = */ 2 11
! assert 23 = */ 23
! assert 24 = */ 3 2 2 2
! assert 25 = */ 5 5
! assert 26 = */ 2 13
! assert 27 = */ 3 3 3
! assert 28 = */ 2 2 7
! assert 29 = */ 29
! assert 30 = */ 5 2 3
! assert 31 = */ 31
! assert 32 = */ 2 2 2 2 2
! assert 33 = */ 3 11
! assert 34 = */ 2 17
! assert 35 = */ 5 7
! assert 36 = */ 3 3 2 2
! assert 37 = */ 37
! assert 38 = */ 2 19
! assert 39 = */ 3 13
! assert 40 = */ 5 2 2 2
module prime_mod
! sieve_table stores 0 in prime numbers, and a prime factor in composites.
integer, dimension(:), allocatable :: sieve_table
private :: PrimeQ
contains
! setup routine must be called first!
subroutine sieve(n) ! populate sieve_table. If n is 0 it deallocates storage, invalidating sieve_table.
integer, intent(in) :: n
integer :: status, i, j
if ((n .lt. 1) .or. allocated(sieve_table)) deallocate(sieve_table)
if (n .lt. 1) return
allocate(sieve_table(n), stat=status)
if (status .ne. 0) stop 'cannot allocate space'
sieve_table(1) = 1
do i=2,int(sqrt(real(n)))+1
if (sieve_table(i) .eq. 0) then
do j = i*i, n, i
sieve_table(j) = i
end do
end if
end do
end subroutine sieve
subroutine check_sieve(n)
integer, intent(in) :: n
if (.not. (allocated(sieve_table) .and. ((1 .le. n) .and. (n .le. size(sieve_table))))) stop 'Call sieve first'
end subroutine check_sieve
logical function isPrime(p)
integer, intent(in) :: p
call check_sieve(p)
isPrime = PrimeQ(p)
end function isPrime
logical function isComposite(p)
integer, intent(in) :: p
isComposite = .not. isPrime(p)
end function isComposite
logical function PrimeQ(p)
integer, intent(in) :: p
PrimeQ = sieve_table(p) .eq. 0
end function PrimeQ
subroutine prime_factors(p, rv, n)
integer, intent(in) :: p ! number to factor
integer, dimension(:), intent(out) :: rv ! the prime factors
integer, intent(out) :: n ! number of factors returned
integer :: i, m
call check_sieve(p)
m = p
i = 1
if (p .ne. 1) then
do while ((.not. PrimeQ(m)) .and. (i .lt. size(rv)))
rv(i) = sieve_table(m)
m = m/rv(i)
i = i+1
end do
end if
if (i .le. size(rv)) rv(i) = m
n = i
end subroutine prime_factors
end module prime_mod
program count_in_factors
use prime_mod
integer :: i, n
integer, dimension(8) :: factors
call sieve(40) ! setup
do i=1,40
factors = 0
call prime_factors(i, factors, n)
write(6,*)'assert',i,'= */',factors(:n)
end do
call sieve(0) ! release memory
end program count_in_factors
FreeBASIC
' FB 1.05.0 Win64
Sub getPrimeFactors(factors() As UInteger, n As UInteger)
If n < 2 Then Return
Dim factor As UInteger = 2
Do
If n Mod factor = 0 Then
Redim Preserve factors(0 To UBound(factors) + 1)
factors(UBound(factors)) = factor
n \= factor
If n = 1 Then Return
Else
factor += 1
End If
Loop
End Sub
Dim factors() As UInteger
For i As UInteger = 1 To 20
Print Using "##"; i;
Print " = ";
If i > 1 Then
Erase factors
getPrimeFactors factors(), i
For j As Integer = LBound(factors) To UBound(factors)
Print factors(j);
If j < UBound(factors) Then Print " x ";
Next j
Print
Else
Print i
End If
Next i
Print
Print "Press any key to quit"
Sleep
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5
Frink
Frink's factoring routines work on arbitrarily-large integers.
i = 1
while true
{
println[join[" x ", factorFlat[i]]]
i = i + 1
}FutureBasic
local fn Factorial( num as long ) as CFStringRef
CFStringRef x, f, result
long fct
f = @"" : x = @""
if num = 1 then result = @" 1" : exit fn
fct = 2
while ( fct <= num )
if ( num mod fct == 0 )
f = fn StringWithFormat( @"%@%@%@", f, x, str( fct ) )
x = @" x"
num = num / fct
else
fct++
end if
wend
result = f
end fn = result
long i
for i = 1 to 20
printf @"%2ld =%@", i, fn Factorial(i)
next
HandleEvents- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
The Factor expression reduces to a list of the primer factors of a given number.
We cannot create the multiplication directly, because it would be reduced immediately to its value. We can make use of the reflection capabilities:
Go
package main
import "fmt"
func main() {
fmt.Println("1: 1")
for i := 2; ; i++ {
fmt.Printf("%d: ", i)
var x string
for n, f := i, 2; n != 1; f++ {
for m := n % f; m == 0; m = n % f {
fmt.Print(x, f)
x = "×"
n /= f
}
}
fmt.Println()
}
}
- 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 ...
Groovy
def factors(number) {
if (number == 1) {
return [1]
}
def factors = []
BigInteger value = number
BigInteger possibleFactor = 2
while (possibleFactor <= value) {
if (value % possibleFactor == 0) {
factors << possibleFactor
value /= possibleFactor
} else {
possibleFactor++
}
}
factors
}
Number.metaClass.factors = { factors(delegate) }
((1..10) + (6351..6359)).each { number ->
println "$number = ${number.factors().join(' x ')}"
}
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 6351 = 3 x 29 x 73 6352 = 2 x 2 x 2 x 2 x 397 6353 = 6353 6354 = 2 x 3 x 3 x 353 6355 = 5 x 31 x 41 6356 = 2 x 2 x 7 x 227 6357 = 3 x 13 x 163 6358 = 2 x 11 x 17 x 17 6359 = 6359
Haskell
Using factorize function from the prime decomposition task,
import Data.List (intercalate)
showFactors n = show n ++ " = " ++ (intercalate " * " . map show . factorize) n
-- Pointfree form
showFactors = ((++) . show) <*> ((" = " ++) . intercalate " * " . map show . factorize)
isPrime n = n > 1 && noDivsBy primeNums n
- Output:
Main> print 1 >> mapM_ (putStrLn . showFactors) [2..]
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
. . .
Main> mapM_ (putStrLn . showFactors) [2144..]
2144 = 2 * 2 * 2 * 2 * 2 * 67
2145 = 3 * 5 * 11 * 13
2146 = 2 * 29 * 37
2147 = 19 * 113
2148 = 2 * 2 * 3 * 179
2149 = 7 * 307
2150 = 2 * 5 * 5 * 43
2151 = 3 * 3 * 239
2152 = 2 * 2 * 2 * 269
2153 = 2153
2154 = 2 * 3 * 359
. . .
Main> mapM_ (putStrLn . showFactors) [121231231232155..]
121231231232155 = 5 * 11 * 419 * 5260630559
121231231232156 = 2 * 2 * 97 * 1061 * 294487867
121231231232157 = 3 * 3 * 3 * 131 * 34275157261
121231231232158 = 2 * 19 * 67 * 1231 * 38681033
121231231232159 = 121231231232159
121231231232160 = 2 * 2 * 2 * 2 * 2 * 3 * 5 * 7 * 7 * 5154389083
121231231232161 = 121231231232161
121231231232162 = 2 * 60615615616081
121231231232163 = 3 * 13 * 83 * 191089 * 195991
121231231232164 = 2 * 2 * 253811 * 119410931
121231231232165 = 5 * 137 * 176979899609
. . .
The real solution seems to have to be some sort of a segmented offset sieve of Eratosthenes, storing factors in array's cells instead of just marks. That way the speed of production might not be diminishing as much.
Icon and Unicon
- 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 ] ...
IS-BASIC
100 PROGRAM "Factors.bas"
110 FOR I=1 TO 30
120 PRINT I;"= ";FACTORS$(I)
130 NEXT
140 DEF FACTORS$(N)
150 LET F$=""
160 IF N=1 THEN
170 LET FACTORS$="1"
180 ELSE
190 LET P=2
200 DO WHILE P<=N
210 IF MOD(N,P)=0 THEN
220 LET F$=F$&STR$(P)&"*"
230 LET N=INT(N/P)
240 ELSE
250 LET P=P+1
260 END IF
270 LOOP
280 LET FACTORS$=F$(1:LEN(F$)-1)
290 END IF
300 END DEF- 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 19 = 19 20 = 2*2*5 21 = 3*7 22 = 2*11 23 = 23 24 = 2*2*2*3 25 = 5*5 26 = 2*13 27 = 3*3*3 28 = 2*2*7 29 = 29 30 = 2*3*5
J
Solution:Use J's factoring primitive,
q:
Example (including formatting):
('1 : 1',":&> ,"1 ': ',"1 ":@q:) 2+i.10
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
Java
public class CountingInFactors{
public static void main(String[] args){
for(int i = 1; i<= 10; i++){
System.out.println(i + " = "+ countInFactors(i));
}
for(int i = 9991; i <= 10000; i++){
System.out.println(i + " = "+ countInFactors(i));
}
}
private static String countInFactors(int n){
if(n == 1) return "1";
StringBuilder sb = new StringBuilder();
n = checkFactor(2, n, sb);
if(n == 1) return sb.toString();
n = checkFactor(3, n, sb);
if(n == 1) return sb.toString();
for(int i = 5; i <= n; i+= 2){
if(i % 3 == 0)continue;
n = checkFactor(i, n, sb);
if(n == 1)break;
}
return sb.toString();
}
private static int checkFactor(int mult, int n, StringBuilder sb){
while(n % mult == 0 ){
if(sb.length() > 0) sb.append(" x ");
sb.append(mult);
n /= mult;
}
return n;
}
}
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 9991 = 97 x 103 9992 = 2 x 2 x 2 x 1249 9993 = 3 x 3331 9994 = 2 x 19 x 263 9995 = 5 x 1999 9996 = 2 x 2 x 3 x 7 x 7 x 17 9997 = 13 x 769 9998 = 2 x 4999 9999 = 3 x 3 x 11 x 101 10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
JavaScript
for(i = 1; i <= 10; i++)
console.log(i + " : " + factor(i).join(" x "));
function factor(n) {
var factors = [];
if (n == 1) return [1];
for(p = 2; p <= n; ) {
if((n % p) == 0) {
factors[factors.length] = p;
n /= p;
}
else p++;
}
return factors;
}
- Output:
1 : 1 2 : 2 3 : 3 4 : 2 x 2 5 : 5 6 : 2 x 3 7 : 7 8 : 2 x 2 x 2 9 : 3 x 3 10 : 2 x 5
jq
Works with gojq, the Go implementation of jq
The following uses `factors/0`, a suitable implementation of which may be found at Prime_decomposition#jq.
gojq supports unlimited-precision integer arithmetic, but the C implementation of jq currently uses IEEE 754 64-bit numbers, so using the latter, the following program will only be reliable for integers up to and including 9,007,199,254,740,992 (2^53). However, "factors" could be easily modified to work with a "BigInt" library for jq, such as BigInt.jq.
# To take advantage of gojq's arbitrary-precision integer arithmetic:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
# Input: a non-negative integer determining when to stop
def count_in_factors:
"1: 1",
(range(2;.) | "\(.): \([factors] | join("x"))");
def count_in_factors($m;$n):
if . == 1 then "1: 1" else empty end,
(range($m;$n) | "\(.): \([factors] | join("x"))");Examples
10 | count_in_factors,
"",
count_in_factors(2144; 2145),
"",
(2|power(100) | count_in_factors(.; .+ 2))- Output:
The output shown here is based on a run of gojq.
1: 1 2: 2 3: 3 4: 2x2 5: 5 6: 2x3 7: 7 8: 2x2x2 9: 3x3 2144: 2x2x2x2x2x67 1267650600228229401496703205376: 2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2 1267650600228229401496703205377: 17x401x61681x340801x2787601x3173389601
Julia
using Primes, Printf
function strfactor(n::Integer)
n > -2 || return "-1 × " * strfactor(-n)
isprime(n) || n < 2 && return dec(n)
f = factor(Vector{typeof(n)}, n)
return join(f, " × ")
end
lo, hi = -4, 40
println("Factor print $lo to $hi:")
for n in lo:hi
@printf("%5d = %s\n", n, strfactor(n))
end
- Output:
Factor print -4 to 40:
-4 = -1 × 2 × 2
-3 = -1 × 3
-2 = -1 × 2
-1 = -1
0 = 0
1 = 1
2 = 2
3 = 3
4 = 2 × 2
5 = 5
6 = 2 × 3
7 = 7
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
11 = 11
12 = 2 × 2 × 3
13 = 13
14 = 2 × 7
15 = 3 × 5
16 = 2 × 2 × 2 × 2
17 = 17
18 = 2 × 3 × 3
19 = 19
20 = 2 × 2 × 5
21 = 3 × 7
22 = 2 × 11
23 = 23
24 = 2 × 2 × 2 × 3
25 = 5 × 5
26 = 2 × 13
27 = 3 × 3 × 3
28 = 2 × 2 × 7
29 = 29
30 = 2 × 3 × 5
31 = 31
32 = 2 × 2 × 2 × 2 × 2
33 = 3 × 11
34 = 2 × 17
35 = 5 × 7
36 = 2 × 2 × 3 × 3
37 = 37
38 = 2 × 19
39 = 3 × 13
40 = 2 × 2 × 2 × 5
Kotlin
// version 1.1.2
fun isPrime(n: Int) : Boolean {
if (n < 2) return false
if (n % 2 == 0) return n == 2
if (n % 3 == 0) return n == 3
var d = 5
while (d * d <= n) {
if (n % d == 0) return false
d += 2
if (n % d == 0) return false
d += 4
}
return true
}
fun getPrimeFactors(n: Int): List<Int> {
val factors = mutableListOf<Int>()
if (n < 1) return factors
if (n == 1 || isPrime(n)) {
factors.add(n)
return factors
}
var factor = 2
var nn = n
while (true) {
if (nn % factor == 0) {
factors.add(factor)
nn /= factor
if (nn == 1) return factors
if (isPrime(nn)) factor = nn
}
else if (factor >= 3) factor += 2
else factor = 3
}
}
fun main(args: Array<String>) {
val list = (MutableList(22) { it + 1 } + 2144) + 6358
for (i in list)
println("${"%4d".format(i)} = ${getPrimeFactors(i).joinToString(" * ")}")
}
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 12 = 2 * 2 * 3 13 = 13 14 = 2 * 7 15 = 3 * 5 16 = 2 * 2 * 2 * 2 17 = 17 18 = 2 * 3 * 3 19 = 19 20 = 2 * 2 * 5 21 = 3 * 7 22 = 2 * 11 2144 = 2 * 2 * 2 * 2 * 2 * 67 6358 = 2 * 11 * 17 * 17
Liberty BASIC
'see Run BASIC solution
for i = 1000 to 1016
print i;" = "; factorial$(i)
next
wait
function factorial$(num)
if num = 1 then factorial$ = "1"
fct = 2
while fct <= num
if (num mod fct) = 0 then
factorial$ = factorial$ ; x$ ; fct
x$ = " x "
num = num / fct
else
fct = fct + 1
end if
wend
end function- Output:
1000 = 2 x 2 x 2 x 5 x 5 x 5 1001 = 7 x 11 x 13 1002 = 2 x 3 x 167 1003 = 17 x 59 1004 = 2 x 2 x 251 1005 = 3 x 5 x 67 1006 = 2 x 503 1007 = 19 x 53 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7 1009 = 1009 1010 = 2 x 5 x 101 1011 = 3 x 337 1012 = 2 x 2 x 11 x 23 1013 = 1013 1014 = 2 x 3 x 13 x 13 1015 = 5 x 7 x 29 1016 = 2 x 2 x 2 x 127
Lua
function factorize( n )
if n == 1 then return {1} end
local k = 2
res = {}
while n > 1 do
while n % k == 0 do
res[#res+1] = k
n = n / k
end
k = k + 1
end
return res
end
for i = 1, 22 do
io.write( i, ": " )
fac = factorize( i )
io.write( fac[1] )
for j = 2, #fac do
io.write( " * ", fac[j] )
end
print ""
end
M2000 Interpreter
Decompose function now return array (in number decomposition task return an inventory list).
Module Count_in_factors {
Inventory Known1=2@, 3@
IsPrime=lambda Known1 (x as decimal) -> {
=0=1
if exist(Known1, x) then =1=1 : exit
if x<=5 OR frac(x) then {if x == 2 OR x == 3 OR x == 5 then Append Known1, x : =1=1
Break}
if frac(x/2) else exit
if frac(x/3) else exit
x1=sqrt(x):d = 5@
{if frac(x/d ) else exit
d += 2: if d>x1 then Append Known1, x : =1=1 : exit
if frac(x/d) else exit
d += 4: if d<= x1 else Append Known1, x : =1=1: exit
loop
}
}
decompose=lambda IsPrime (n as decimal) -> {
Factors=(,)
{
k=2@
While frac(n/k)=0
n/=k
Append Factors, (k,)
End While
if n=1 then exit
k++
While frac(n/k)=0
n/=k
Append Factors, (k,)
End While
if n=1 then exit
{
k+=2
while not isprime(k) {k+=2}
While frac(n/k)=0
n/=k : Append Factors, (k,)
End While
if n=1 then exit
loop
}
}
=Factors
}
fold=lambda (a, f$)->{
Push if$(len(f$)=0->f$, f$+"x")+str$(a,"")
}
Print "1=1"
i=1@
do
i++
Print str$(i,"")+"="+Decompose(i)#fold$(fold,"")
always
}
Count_in_factorsM4
define(`for',
`ifelse($#,0,``$0'',
`ifelse(eval($2<=$3),1,
`pushdef(`$1',$2)$5`'popdef(`$1')$0(`$1',eval($2+$4),$3,$4,`$5')')')')dnl
define(`by',
`ifelse($1,$2,
$1,
`ifelse(eval($1%$2==0),1,
`$2 x by(eval($1/$2),$2)',
`by($1,eval($2+1))') ') ')dnl
define(`wby',
`$1 = ifelse($1,1,
$1,
`by($1,2)') ')dnl
for(`y',1,25,1, `wby(y)
')- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5 21 = 3 x 7 22 = 2 x 11 23 = 23 24 = 2 x 2 x 2 x 3 25 = 5 x 5
Maple
factorNum := proc(n)
local i, j, firstNum;
if n = 1 then
printf("%a", 1);
end if;
firstNum := true:
for i in ifactors(n)[2] do
for j to i[2] do
if firstNum then
printf ("%a", i[1]);
firstNum := false:
else
printf(" x %a", i[1]);
end if;
end do;
end do;
printf("\n");
return NULL;
end proc:
for i from 1 to 10 do
printf("%2a: ", i);
factorNum(i);
end do;- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 10: 2 x 5
Mathematica / Wolfram Language
n = 2;
While[n < 100,
Print[Row[Riffle[Flatten[Map[Apply[ConstantArray, #] &, FactorInteger[n]]],"*"]]];
n++]
NetRexx
/* NetRexx */
options replace format comments java crossref symbols nobinary
runSample(arg)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method factor(val) public static
rv = 1
if val > 1 then do
rv = ''
loop n_ = val until n_ = 1
parse checkFactor(2, n_, rv) n_ rv
if n_ = 1 then leave n_
parse checkFactor(3, n_, rv) n_ rv
if n_ = 1 then leave n_
loop m_ = 5 to n_ by 2 until n_ = 1
if m_ // 3 = 0 then iterate m_
parse checkFactor(m_, n_, rv) n_ rv
end m_
end n_
end
return rv
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method checkFactor(mult = long, n_ = long, fac) private static binary
msym = 'x'
loop while n_ // mult = 0
fac = fac msym mult
n_ = n_ % mult
end
fac = (fac.strip).strip('l', msym).space
return n_ fac
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
-- input is a list of pairs of numbers - no checking is done
if arg = '' then arg = '1 11 89 101 1000 1020 10000 10010'
loop while arg \= ''
parse arg lv rv arg
say
say '-'.copies(60)
say lv.right(8) 'to' rv
say '-'.copies(60)
loop fv = lv to rv
fac = factor(fv)
pv = ''
if fac.words = 1 & fac \= 1 then pv = '<prime>'
say fv.right(8) '=' fac pv
end fv
end
return
- Output:
------------------------------------------------------------
1 to 11
------------------------------------------------------------
1 = 1
2 = 2 <prime>
3 = 3 <prime>
4 = 2 x 2
5 = 5 <prime>
6 = 2 x 3
7 = 7 <prime>
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11 <prime>
------------------------------------------------------------
89 to 101
------------------------------------------------------------
89 = 89 <prime>
90 = 2 x 3 x 3 x 5
91 = 7 x 13
92 = 2 x 2 x 23
93 = 3 x 31
94 = 2 x 47
95 = 5 x 19
96 = 2 x 2 x 2 x 2 x 2 x 3
97 = 97 <prime>
98 = 2 x 7 x 7
99 = 3 x 3 x 11
100 = 2 x 2 x 5 x 5
101 = 101 <prime>
------------------------------------------------------------
1000 to 1020
------------------------------------------------------------
1000 = 2 x 2 x 2 x 5 x 5 x 5
1001 = 7 x 11 x 13
1002 = 2 x 3 x 167
1003 = 17 x 59
1004 = 2 x 2 x 251
1005 = 3 x 5 x 67
1006 = 2 x 503
1007 = 19 x 53
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
1009 = 1009 <prime>
1010 = 2 x 5 x 101
1011 = 3 x 337
1012 = 2 x 2 x 11 x 23
1013 = 1013 <prime>
1014 = 2 x 3 x 13 x 13
1015 = 5 x 7 x 29
1016 = 2 x 2 x 2 x 127
1017 = 3 x 3 x 113
1018 = 2 x 509
1019 = 1019 <prime>
1020 = 2 x 2 x 3 x 5 x 17
------------------------------------------------------------
10000 to 10010
------------------------------------------------------------
10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
10001 = 73 x 137
10002 = 2 x 3 x 1667
10003 = 7 x 1429
10004 = 2 x 2 x 41 x 61
10005 = 3 x 5 x 23 x 29
10006 = 2 x 5003
10007 = 10007 <prime>
10008 = 2 x 2 x 2 x 3 x 3 x 139
10009 = 10009 <prime>
10010 = 2 x 5 x 7 x 11 x 13
Nim
var primes = newSeq[int]()
proc getPrime(idx: int): int =
if idx >= primes.len:
if primes.len == 0:
primes.add 2
primes.add 3
var last = primes[primes.high]
while idx >= primes.len:
last += 2
for i, p in primes:
if p * p > last:
primes.add last
break
if last mod p == 0:
break
return primes[idx]
for x in 1 ..< int32.high.int:
stdout.write x, " = "
var n = x
var first = true
for i in 0 ..< int32.high:
let p = getPrime(i)
while n mod p == 0:
n = n div p
if not first: stdout.write " x "
first = false
stdout.write p
if n <= p * p:
break
if first > 0: echo n
elif n > 1: echo " x ", n
else: echo ""
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 ...
Objeck
class CountingInFactors {
function : Main(args : String[]) ~ Nil {
for(i := 1; i <= 10; i += 1;){
count := CountInFactors(i);
("{$i} = {$count}")->PrintLine();
};
for(i := 9991; i <= 10000; i += 1;){
count := CountInFactors(i);
("{$i} = {$count}")->PrintLine();
};
}
function : CountInFactors(n : Int) ~ String {
if(n = 1) {
return "1";
};
sb := "";
n := CheckFactor(2, n, sb);
if(n = 1) {
return sb;
};
n := CheckFactor(3, n, sb);
if(n = 1) {
return sb;
};
for(i := 5; i <= n; i += 2;) {
if(i % 3 <> 0) {
n := CheckFactor(i, n, sb);
if(n = 1) {
break;
};
};
};
return sb;
}
function : CheckFactor(mult : Int, n : Int, sb : String) ~ Int {
while(n % mult = 0 ) {
if(sb->Size() > 0) {
sb->Append(" x ");
};
sb->Append(mult);
n /= mult;
};
return n;
}
}Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 9991 = 97 x 103 9992 = 2 x 2 x 2 x 1249 9993 = 3 x 3331 9994 = 2 x 19 x 263 9995 = 5 x 1999 9996 = 2 x 2 x 3 x 7 x 7 x 17 9997 = 13 x 769 9998 = 2 x 4999 9999 = 3 x 3 x 11 x 101 10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
OCaml
open Big_int
let prime_decomposition x =
let rec inner c p =
if lt_big_int p (square_big_int c) then
[p]
else if eq_big_int (mod_big_int p c) zero_big_int then
c :: inner c (div_big_int p c)
else
inner (succ_big_int c) p
in
inner (succ_big_int (succ_big_int zero_big_int)) x
let () =
let rec aux v =
let ps = prime_decomposition v in
print_string (string_of_big_int v);
print_string " = ";
print_endline (String.concat " x " (List.map string_of_big_int ps));
aux (succ_big_int v)
in
aux unit_big_int
- Execution:
$ ocamlopt -o count.opt nums.cmxa count.ml $ ./count.opt 1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 ... 6351 = 3 x 29 x 73 6352 = 2 x 2 x 2 x 2 x 397 6353 = 6353 6354 = 2 x 3 x 3 x 353 6355 = 5 x 31 x 41 6356 = 2 x 2 x 7 x 227 6357 = 3 x 13 x 163 6358 = 2 x 11 x 17 x 17 6359 = 6359 ^C
Octave
Octave's factor function returns an array:
for (n = 1:20)
printf ("%i: ", n)
printf ("%i ", factor (n))
printf ("\n")
endfor
- 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 19: 19 20: 2 2 5
PARI/GP
fnice(n)={
my(f,s="",s1);
if (n < 2, return(n));
f = factor(n);
s = Str(s, f[1,1]);
if (f[1, 2] != 1, s=Str(s, "^", f[1,2]));
for(i=2,#f[,1], s1 = Str(" * ", f[i, 1]); if (f[i, 2] != 1, s1 = Str(s1, "^", f[i, 2])); s = Str(s, s1));
s
};
n=0;while(n++<21, printf("%2s: %s\n",n,fnice(n)))- Output:
1: 1 2: 2 3: 3 4: 2^2 5: 5 6: 2 * 3 7: 7 8: 2^3 9: 3^2 10: 2 * 5 11: 11 12: 2^2 * 3 13: 13 14: 2 * 7 15: 3 * 5 16: 2^4 17: 17 18: 2 * 3^2 19: 19 20: 2^2 * 5
Pascal
program CountInFactors(output);
{$IFDEF FPC}
{$MODE DELPHI}
{$ENDIF}
type
TdynArray = array of integer;
function factorize(number: integer): TdynArray;
var
k: integer;
begin
if number = 1 then
begin
setlength(Result, 1);
Result[0] := 1
end
else
begin
k := 2;
while number > 1 do
begin
while number mod k = 0 do
begin
setlength(Result, length(Result) + 1);
Result[high(Result)] := k;
number := number div k;
end;
inc(k);
end;
end
end;
var
i, j: integer;
fac: TdynArray;
begin
for i := 1 to 22 do
begin
write(i, ': ' );
fac := factorize(i);
write(fac[0]);
for j := 1 to high(fac) do
write(' * ', fac[j]);
writeln;
end;
end.
- 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 19: 19 20: 2 * 2 * 5 21: 3 * 7 22: 2 * 11
PascalABC.NET
// https://rosettacode.org/wiki/Count_in_factors#PascalABC.NET
function Factorize(x: integer): List<integer>;
begin
Result := new List<integer>;
if x = 1 then
begin
Result.Add(1);
exit
end;
var i := 2;
repeat
if x.Divs(i) then
begin
Result.Add(i);
x := x div i;
end
else i += 1;
until x = 1;
end;
begin
var n := 22;
(1..n).PrintLines(x -> $'{x,3}: {Factorize(x).JoinToString('' * '')}')
end.
- Output:
1: 1 2: 2 3: 3 4: 2 * 2 5: 5 6: 2 * 3 7: 7 8: 2 * 2 * 2 9: 3 * 3 10: 2 * 5 11: 11 12: 2 * 2 * 3 13: 13 14: 2 * 7 15: 3 * 5 16: 2 * 2 * 2 * 2 17: 17 18: 2 * 3 * 3 19: 19 20: 2 * 2 * 5 21: 3 * 7 22: 2 * 11
Perl
Typically one would use a module for this. Note that these modules all return an empty list for '1'. This should be efficient to 50+ digits:
use ntheory qw/factor/;
print "$_ = ", join(" x ", factor($_)), "\n" for 1000000000000000000 .. 1000000000000000010;
- Output:
1000000000000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 1000000000000000001 = 101 x 9901 x 999999000001 1000000000000000002 = 2 x 3 x 17 x 131 x 1427 x 52445056723 1000000000000000003 = 1000000000000000003 1000000000000000004 = 2 x 2 x 1801 x 246809 x 562425889 1000000000000000005 = 3 x 5 x 44087 x 691381 x 2187161 1000000000000000006 = 2 x 7 x 919 x 77724234416291 1000000000000000007 = 1370531 x 729644203597 1000000000000000008 = 2 x 2 x 2 x 3 x 3 x 97 x 26209 x 32779 x 166667 1000000000000000009 = 1000000000000000009 1000000000000000010 = 2 x 5 x 11 x 103 x 4013 x 21993833369
Giving similar output and also good for large inputs:
use Math::Pari qw/factorint/;
sub factor {
my ($pn,$pc) = @{Math::Pari::factorint(shift)};
return map { ($pn->[$_]) x $pc->[$_] } 0 .. $#$pn;
}
print "$_ = ", join(" x ", factor($_)), "\n" for 1000000000000000000 .. 1000000000000000010;
or, somewhat slower and limited to native 32-bit or 64-bit integers only:
use Math::Factor::XS qw/prime_factors/;
print "$_ = ", join(" x ", prime_factors($_)), "\n" for 1000000000000000000 .. 1000000000000000010;
If we want to implement it self-contained, we could use the prime decomposition routine from the Prime_decomposition task. This is reasonably fast and small, though much slower than the modules and certainly could have more optimization.
sub factors {
my($n, $p, @out) = (shift, 3);
return if $n < 1;
while (!($n&1)) { $n >>= 1; push @out, 2; }
while ($n > 1 && $p*$p <= $n) {
while ( ($n % $p) == 0) {
$n /= $p;
push @out, $p;
}
$p += 2;
}
push @out, $n if $n > 1;
@out;
}
print "$_ = ", join(" x ", factors($_)), "\n" for 100000000000 .. 100000000100;
We could use the second extensible sieve from Sieve_of_Eratosthenes#Extensible_sieves to only divide by primes.
tie my @primes, 'Tie::SieveOfEratosthenes';
sub factors {
my($n, $i, $p, @out) = (shift, 0, 2);
while ($n >= $p * $p) {
while ($n % $p == 0) {
push @out, $p;
$n /= $p;
}
$p = $primes[++$i];
}
push @out, $n if $n > 1 || !@out;
@out;
}
print "$_ = ", join(" x ", factors($_)), "\n" for 100000000000 .. 100000000010;
- Output:
100000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 100000000001 = 11 x 11 x 23 x 4093 x 8779 100000000002 = 2 x 3 x 7 x 1543 x 1543067 100000000003 = 100000000003 100000000004 = 2 x 2 x 17573 x 1422637 100000000005 = 3 x 5 x 19 x 1627 x 215659 100000000006 = 2 x 3947 x 12667849 100000000007 = 353 x 283286119 100000000008 = 2 x 2 x 2 x 3 x 3 x 3 x 462962963 100000000009 = 7 x 13 x 53 x 1979 x 10477 100000000010 = 2 x 5 x 101 x 3541 x 27961
This next example isn't quite as fast and uses much more memory, but it is self-contained and shows a different approach. As written it must start at 1, but a range can be handled by using a map to prefill the p_and_sq array.
#!perl -C
use utf8;
use strict;
use warnings;
my $limit = 1000;
print "$_ = $_\n" for 1..3;
my @p_and_sq = ( [2, 4], [3, 9] );
N: for my $n ( 4 .. 1000 ) {
print $n, " = ";
for( my $i = 0; $i <= $#p_and_sq; ++$i ) {
my ($p, $sq) = @{ $p_and_sq[$i] };
if( $sq > $n ) {
print $n, "\n";
push @p_and_sq, [ $n, $n*$n ];
next N;
}
while( 0 == ($n % $p) ) {
print $p;
$n /= $p;
if( $n == 1 ) {
print "\n";
next N;
}
print " × ";
}
}
die "Ran out of primes?!";
}
Phix
with javascript_semantics procedure factorise(integer n) sequence res = prime_factors(n,true) res = join(apply(res,sprint)," x ") printf(1,"%2d: %s\n",{n,res}) end procedure papply(tagset(10)&{2144,1000000000},factorise)
- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 10: 2 x 5 2144: 2 x 2 x 2 x 2 x 2 x 67 1000000000: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
PicoLisp
This is the 'factor' function from Prime decomposition#PicoLisp.
(de factor (N)
(make
(let (D 2 L (1 2 2 . (4 2 4 2 4 6 2 6 .)) M (sqrt N))
(while (>= M D)
(if (=0 (% N D))
(setq M (sqrt (setq N (/ N (link D)))))
(inc 'D (pop 'L)) ) )
(link N) ) ) )
(for N 20
(prinl N ": " (glue " * " (factor N))) )- Output:
1: 1 2: 2 3: 3 4: 2 * 2 5: 5 6: 2 * 3 7: 7 8: 2 * 2 * 2 9: 3 * 3 10: 2 * 5 11: 11 12: 2 * 2 * 3 13: 13 14: 2 * 7 15: 3 * 5 16: 2 * 2 * 2 * 2 17: 17 18: 2 * 3 * 3 19: 19 20: 2 * 2 * 5
PL/I
cnt: procedure options (main);
declare (i, k, n) fixed binary;
declare first bit (1) aligned;
do n = 1 to 40;
put skip list (n || ' =');
k = n; first = '1'b;
repeat:
do i = 2 to k-1;
if mod(k, i) = 0 then
do;
k = k/i;
if ^first then put edit (' x ')(A);
first = '0'b;
put edit (trim(i)) (A);
go to repeat;
end;
end;
if ^first then put edit (' x ')(A);
if n = 1 then i = 1;
put edit (trim(i)) (A);
end;
end cnt;Results:
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17 = 17
18 = 2 x 3 x 3
19 = 19
20 = 2 x 2 x 5
21 = 3 x 7
22 = 2 x 11
23 = 23
24 = 2 x 2 x 2 x 3
25 = 5 x 5
26 = 2 x 13
27 = 3 x 3 x 3
28 = 2 x 2 x 7
29 = 29
30 = 2 x 3 x 5
31 = 31
32 = 2 x 2 x 2 x 2 x 2
33 = 3 x 11
34 = 2 x 17
35 = 5 x 7
36 = 2 x 2 x 3 x 3
37 = 37
38 = 2 x 19
39 = 3 x 13
40 = 2 x 2 x 2 x 5
PowerShell
function eratosthenes ($n) {
if($n -ge 1){
$prime = @(1..($n+1) | foreach{$true})
$prime[1] = $false
$m = [Math]::Floor([Math]::Sqrt($n))
for($i = 2; $i -le $m; $i++) {
if($prime[$i]) {
for($j = $i*$i; $j -le $n; $j += $i) {
$prime[$j] = $false
}
}
}
1..$n | where{$prime[$_]}
} else {
"$n must be equal or greater than 1"
}
}
function prime-decomposition ($n) {
$array = eratosthenes $n
$prime = @()
foreach($p in $array) {
while($n%$p -eq 0) {
$n /= $p
$prime += @($p)
}
}
$prime
}
$OFS = " x "
"$(prime-decomposition 2144)"
"$(prime-decomposition 100)"
"$(prime-decomposition 12)"
Output:
2 x 2 x 2 x 2 x 2 x 67 2 x 2 x 5 x 5 2 x 2 x 3
PureBasic
Procedure Factorize(Number, List Factors())
Protected I = 3, Max
ClearList(Factors())
While Number % 2 = 0
AddElement(Factors())
Factors() = 2
Number / 2
Wend
Max = Number
While I <= Max And Number > 1
While Number % I = 0
AddElement(Factors())
Factors() = I
Number / I
Wend
I + 2
Wend
EndProcedure
If OpenConsole()
NewList n()
For a=1 To 20
text$=RSet(Str(a),2)+"= "
Factorize(a,n())
If ListSize(n())
ResetList(n())
While NextElement(n())
text$ + Str(n())
If ListSize(n())-ListIndex(n())>1
text$ + "*"
EndIf
Wend
Else
text$+Str(a) ; To handle the '1', which is not really a prime...
EndIf
PrintN(text$)
Next a
EndIf
- 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 19= 19 20= 2*2*5
Python
This uses the functools.lru_cache standard library module to cache intermediate results.
from functools import lru_cache
primes = [2, 3, 5, 7, 11, 13, 17] # Will be extended
@lru_cache(maxsize=2000)
def pfactor(n):
if n == 1:
return [1]
n2 = n // 2 + 1
for p in primes:
if p <= n2:
d, m = divmod(n, p)
if m == 0:
if d > 1:
return [p] + pfactor(d)
else:
return [p]
else:
if n > primes[-1]:
primes.append(n)
return [n]
if __name__ == '__main__':
mx = 5000
for n in range(1, mx + 1):
factors = pfactor(n)
if n <= 10 or n >= mx - 20:
print( '%4i %5s %s' % (n,
'' if factors != [n] or n == 1 else 'prime',
'x'.join(str(i) for i in factors)) )
if n == 11:
print('...')
print('\nNumber of primes gathered up to', n, 'is', len(primes))
print(pfactor.cache_info())
- Output:
1 1 2 prime 2 3 prime 3 4 2x2 5 prime 5 6 2x3 7 prime 7 8 2x2x2 9 3x3 10 2x5 ... 4980 2x2x3x5x83 4981 17x293 4982 2x47x53 4983 3x11x151 4984 2x2x2x7x89 4985 5x997 4986 2x3x3x277 4987 prime 4987 4988 2x2x29x43 4989 3x1663 4990 2x5x499 4991 7x23x31 4992 2x2x2x2x2x2x2x3x13 4993 prime 4993 4994 2x11x227 4995 3x3x3x5x37 4996 2x2x1249 4997 19x263 4998 2x3x7x7x17 4999 prime 4999 5000 2x2x2x5x5x5x5 Number of primes gathered up to 5000 is 669 CacheInfo(hits=3935, misses=7930, maxsize=2000, currsize=2000)
Quackery
Reusing the code from Prime Decomposition.
[ [] swap
dup times
[ [ dup i^ 2 + /mod
0 = while
nip dip
[ i^ 2 + join ]
again ]
drop
dup 1 = if conclude ]
drop ] is primefactors ( n --> [ )
[ 1 dup echo cr
[ 1+ dup primefactors
witheach
[ echo
i if [ say " x " ] ]
cr again ] ] is countinfactors ( --> )
countinfactors- Output:
1 2 3 2 x 2 5 2 x 3 7 2 x 2 x 2 3 x 3 2 x 5 11 2 x 2 x 3 13 2 x 7 3 x 5 2 x 2 x 2 x 2 17 2 x 3 x 3 19 2 x 2 x 5 3 x 7 2 x 11 23
… and so on. Quackery uses bignums, so "… until boredom ensues."
R
#initially I created a function which returns prime factors then I have created another function counts in the factors and #prints the values.
findfactors <- function(num) {
x <- c()
p1<- 2
p2 <- 3
everyprime <- num
while( everyprime != 1 ) {
while( everyprime%%p1 == 0 ) {
x <- c(x, p1)
everyprime <- floor(everyprime/ p1)
}
p1 <- p2
p2 <- p2 + 2
}
x
}
count_in_factors=function(x){
primes=findfactors(x)
x=c(1)
for (i in 1:length(primes)) {
x=paste(primes[i],"x",x)
}
return(x)
}
count_in_factors(72)
- Output:
[1] "3 x 3 x 2 x 2 x 2 x 1"
Racket
See also #Scheme. This uses Racket’s math/number-theory package
#lang typed/racket
(require math/number-theory)
(define (factorise-as-primes [n : Natural])
(if
(= n 1)
'(1)
(let ((F (factorize n)))
(append*
(for/list : (Listof (Listof Natural))
((f (in-list F)))
(make-list (second f) (first f)))))))
(define (factor-count [start-inc : Natural] [end-inc : Natural])
(for ((i : Natural (in-range start-inc (add1 end-inc))))
(define f (string-join (map number->string (factorise-as-primes i)) " × "))
(printf "~a:\t~a~%" i f)))
(factor-count 1 22)
(factor-count 2140 2150)
; tb
- 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 19: 19 20: 2 × 2 × 5 21: 3 × 7 22: 2 × 11 2140: 2 × 2 × 5 × 107 2141: 2141 2142: 2 × 3 × 3 × 7 × 17 2143: 2143 2144: 2 × 2 × 2 × 2 × 2 × 67 2145: 3 × 5 × 11 × 13 2146: 2 × 29 × 37 2147: 19 × 113 2148: 2 × 2 × 3 × 179 2149: 7 × 307 2150: 2 × 5 × 5 × 43
Raku
(formerly Perl 6)
constant @primes = 2, |(3, 5, 7 ... *).grep: *.is-prime;
multi factors(1) { 1 }
multi factors(Int $remainder is copy) {
gather for @primes -> $factor {
# if remainder < factor², we're done
if $factor * $factor > $remainder {
take $remainder if $remainder > 1;
last;
}
# How many times can we divide by this prime?
while $remainder %% $factor {
take $factor;
last if ($remainder div= $factor) === 1;
}
}
}
say "$_: ", factors($_).join(" × ") for 1..*;
The first twenty numbers:
1: 1 2: 2 3: 3 4: 2 × 2 5: 5 6: 2 × 3 7: 7 8: 2 × 2 × 2 9: 3 × 3 10: 2 × 5 11: 11 12: 2 × 2 × 3 13: 13 14: 2 × 7 15: 3 × 5 16: 2 × 2 × 2 × 2 17: 17 18: 2 × 3 × 3 19: 19 20: 2 × 2 × 5
Here we use a multi declaration with a constant parameter to match the degenerate case. We use copy parameters when we wish to reuse the formal parameter as a mutable variable within the function. (Parameters default to readonly in Raku.) Note the use of gather/take as the final statement in the function, which is a common Raku idiom to set up a coroutine within a function to return a lazy list on demand.
Note also the '×' above is not ASCII 'x', but U+00D7 MULTIPLICATION SIGN. Raku does Unicode natively.
Here is a solution inspired from Almost_prime#C. It doesn't use &is-prime.
sub factor($n is copy) {
$n == 1 ?? 1 !!
gather {
$n /= take 2 while $n %% 2;
$n /= take 3 while $n %% 3;
loop (my $p = 5; $p*$p <= $n; $p+=2) {
$n /= take $p while $n %% $p;
}
take $n unless $n == 1;
}
}
say "$_ == ", join " \x00d7 ", factor $_ for 1 .. 20;
Same output as above.
Alternately, use a module:
use Prime::Factor;
say "$_ = {(.&prime-factors || 1).join: ' x ' }" for flat 1 .. 10, 10**20 .. 10**20 + 10;
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 100000000000000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 100000000000000000001 = 73 x 137 x 1676321 x 5964848081 100000000000000000002 = 2 x 3 x 155977777 x 106852828571 100000000000000000003 = 373 x 155773 x 1721071782307 100000000000000000004 = 2 x 2 x 13 x 1597 x 240841 x 4999900001 100000000000000000005 = 3 x 5 x 7 x 7 x 83 x 1663 x 985694468327 100000000000000000006 = 2 x 31 x 6079 x 265323774602147 100000000000000000007 = 67 x 166909 x 8942221889969 100000000000000000008 = 2 x 2 x 2 x 3 x 3 x 3 x 233 x 1986965506278811 100000000000000000009 = 557 x 72937 x 2461483384901 100000000000000000010 = 2 x 5 x 11 x 909090909090909091
Refal
$ENTRY Go {
= <Each Show <Iota 1 15> 2144>;
};
Factorize {
1 = 1;
s.N = <Factorize 2 s.N>;
s.D s.N, <Compare s.N s.D>: '-' = ;
s.D s.N, <Divmod s.N s.D>: {
(s.R) 0 = s.D <Factorize s.D s.R>;
e.X = <Factorize <+ 1 s.D> s.N>;
};
};
Join {
(e.J) = ;
(e.J) s.N = <Symb s.N>;
(e.J) s.N e.X = <Symb s.N> e.J <Join (e.J) e.X>;
};
Iota {
s.End s.End = s.End;
s.Start s.End = s.Start <Iota <+ s.Start 1> s.End>;
};
Each {
s.F = ;
s.F t.I e.X = <Mu s.F t.I> <Each s.F e.X>;
};
Show {
e.N = <Prout <Symb e.N> ' = ' <Join (' x ') <Factorize e.N>>>;
};- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 2144 = 2 x 2 x 2 x 2 x 2 x 67
REXX
Simple approach
As per the task's requirements, the prime factors of 1 (unity) will be listed as 1,
even though, strictly speaking, it should be null. The same applies to 0.
Programming note: if the high argument is negative, its positive value is used and no displaying of the
prime factors are listed, but the number of primes found is always shown. The showing of the count of
primes was included to help verify the factoring (of composites).
/*REXX program lists the prime factors of a specified integer (or a range of integers).*/
@.=left('', 8); @.0="{unity} "; @.1='[prime] ' /*some tags and handy-dandy literals.*/
parse arg LO HI @ . /*get optional arguments from the C.L. */
if LO=='' | LO=="," then do; LO=1; HI=40; end /*Not specified? Then use the default.*/
if HI=='' | HI=="," then HI= LO /* " " " " " " */
if @=='' then @= 'x' /* " " " " " " */
if length(@)\==1 then @= x2c(@) /*Not length 1? Then use hexadecimal. */
tell= (HI>0) /*if HIGH is positive, then show #'s.*/
HI= abs(HI) /*use the absolute value for HIGH. */
w= length(HI) /*get maximum width for pretty output. */
numeric digits max(9, w + 1) /*maybe bump the precision of numbers. */
#= 0 /*the number of primes found (so far). */
do n=abs(LO) to HI; f= factr(n) /*process a single number or a range.*/
p= words( translate(f, ,@) ) - (n==1) /*P: is the number of prime factors. */
if p==1 then #= # + 1 /*bump the primes counter (exclude N=1)*/
if tell then say right(n, w) '=' @.p f /*display if a prime, plus its factors.*/
end /*n*/
say
say right(#, w) ' primes found.' /*display the number of primes found. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: procedure expose @; parse arg z 1 n,$; if z<2 then return z /*is Z too small?*/
do while z//2==0; $= $||@||2; z= z%2; end /*maybe add factor of 2 */
do while z//3==0; $= $||@||3; z= z%3; end /* " " " " 3 */
do while z//5==0; $= $||@||5; z= z%5; end /* " " " " 5 */
do while z//7==0; $= $||@||7; z= z%7; end /* " " " " 7 */
do j=11 by 6 while j<=z /*insure that J isn't divisible by 3.*/
parse var j '' -1 _ /*get the last decimal digit of J. */
if _\==5 then do while z//j==0; $=$||@||j; z= z%j; end /*maybe reduce Z.*/
if _ ==3 then iterate /*Next # ÷ by 5? Skip. ___ */
if j*j>n then leave /*are we higher than the √ N ? */
y= j + 2 /*obtain the next odd divisor. */
do while z//y==0; $=$||@||y; z= z%y; end /*maybe reduce Z.*/
end /*j*/
if z==1 then return substr($, 1+length(@) ) /*Is residual=1? Don't add 1*/
return substr($||@||z, 1+length(@) ) /*elide superfluous header. */
- output when using the default inputs:
1 = {unity} 1
2 = [prime] 2
3 = [prime] 3
4 = 2x2
5 = [prime] 5
6 = 2x3
7 = [prime] 7
8 = 2x2x2
9 = 3x3
10 = 2x5
11 = [prime] 11
12 = 2x2x3
13 = [prime] 13
14 = 2x7
15 = 3x5
16 = 2x2x2x2
17 = [prime] 17
18 = 2x3x3
19 = [prime] 19
20 = 2x2x5
21 = 3x7
22 = 2x11
23 = [prime] 23
24 = 2x2x2x3
25 = 5x5
26 = 2x13
27 = 3x3x3
28 = 2x2x7
29 = [prime] 29
30 = 2x3x5
31 = [prime] 31
32 = 2x2x2x2x2
33 = 3x11
34 = 2x17
35 = 5x7
36 = 2x2x3x3
37 = [prime] 37
38 = 2x19
39 = 3x13
40 = 2x2x2x5
12 primes found.
- output when the following input was used: 1 12 207820
1 = {unity} 1
2 = [prime] 2
3 = [prime] 3
4 = 2 x 2
5 = [prime] 5
6 = 2 x 3
7 = [prime] 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = [prime] 11
12 = 2 x 2 x 3
5 primes found.
- output when the following input was used: 1 -10000
1229 primes found.
- output when the following input was used: 1 -100000
9592 primes found.
Using integer SQRT
This REXX version computes the integer square root of the integer being factor (to limit the range of factors),
this makes this version about 50% faster than the 1st REXX version.
Also, the number of early testing of prime factors was expanded.
Note that the integer square root section of code doesn't use any floating point numbers, just integers.
/*REXX program lists the prime factors of a specified integer (or a range of integers).*/
@.=left('', 8); @.0="{unity} "; @.1='[prime] ' /*some tags and handy-dandy literals.*/
parse arg LO HI @ . /*get optional arguments from the C.L. */
if LO=='' | LO=="," then do; LO=1; HI=40; end /*Not specified? Then use the default.*/
if HI=='' | HI=="," then HI= LO /* " " " " " " */
if @=='' then @= 'x' /* " " " " " " */
if length(@)\==1 then @= x2c(@) /*Not length 1? Then use hexadecimal. */
tell= (HI>0) /*if HIGH is positive, then show #'s.*/
HI= abs(HI) /*use the absolute value for HIGH. */
w= length(HI) /*get maximum width for pretty output. */
numeric digits max(9, w + 1) /*maybe bump the precision of numbers. */
#= 0 /*the number of primes found (so far). */
do n=abs(LO) to HI; f= factr(n) /*process a single number or a range.*/
p= words( translate(f, ,@) ) - (n==1) /*P: is the number of prime factors. */
if p==1 then #= # + 1 /*bump the primes counter (exclude N=1)*/
if tell then say right(n, w) '=' @.p f /*display if a prime, plus its factors.*/
end /*n*/
say
say right(#, w) ' primes found.' /*display the number of primes found. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: procedure expose @; parse arg z 1 n,$; if z<2 then return z /*is Z too small?*/
do while z// 2==0; $= $||@||2 ; z= z%2 ; end /*maybe add factor of 2 */
do while z// 3==0; $= $||@||3 ; z= z%3 ; end /* " " " " 3 */
do while z// 5==0; $= $||@||5 ; z= z%5 ; end /* " " " " 5 */
do while z// 7==0; $= $||@||7 ; z= z%7 ; end /* " " " " 7 */
do while z//11==0; $= $||@||11; z= z%11; end /* " " " " 11 */
do while z//13==0; $= $||@||13; z= z%13; end /* " " " " 13 */
do while z//17==0; $= $||@||17; z= z%17; end /* " " " " 17 */
do while z//19==0; $= $||@||19; z= z%19; end /* " " " " 19 */
do while z//23==0; $= $||@||23; z= z%23; end /* " " " " 23 */
do while z//29==0; $= $||@||29; z= z%29; end /* " " " " 29 */
do while z//31==0; $= $||@||31; z= z%31; end /* " " " " 31 */
do while z//37==0; $= $||@||37; z= z%37; end /* " " " " 37 */
if z>40 then do; t= z; q= 1; r= 0; do while q<=t; q= q * 4
end /*while*/
do while q>1; q=q%4; _=t-r-q; r=r%2; if _>=0 then do; t=_; r=r+q
end
end /*while*/ /* [↑] find integer SQRT(z). */
/*R: is the integer SQRT of Z.*/
do j=41 by 6 to r while j<=z /*insure J isn't divisible by 3*/
parse var j '' -1 _ /*get last decimal digit of J.*/
if _\==5 then do while z//j==0; $=$||@||j; z= z%j; end
if _ ==3 then iterate /*Next number ÷ by 5 ? Skip.*/
y= j + 2 /*use the next (odd) divisor. */
do while z//y==0; $=$||@||y; z= z%y; end
end /*j*/ /* [↑] reduce Z by Y ? */
end /*if z>40*/
if z==1 then return substr($, 1+length(@) ) /*Is residual=1? Don't add 1*/
return substr($||@||z, 1+length(@) ) /*elide superfluous header. */
- output when using the default inputs:
1 = {unity} 1
2 = [prime] 2
3 = [prime] 3
4 = 2∙2
5 = [prime] 5
6 = 2∙3
7 = [prime] 7
8 = 2∙2∙2
9 = 3∙3
10 = 2∙5
11 = [prime] 11
12 = 2∙2∙3
13 = [prime] 13
14 = 2∙7
15 = 3∙5
16 = 2∙2∙2∙2
17 = [prime] 17
18 = 2∙3∙3
19 = [prime] 19
20 = 2∙2∙5
21 = 3∙7
22 = 2∙11
23 = [prime] 23
24 = 2∙2∙2∙3
25 = 5∙5
26 = 2∙13
27 = 3∙3∙3
28 = 2∙2∙7
29 = [prime] 29
30 = 2∙3∙5
31 = [prime] 31
32 = 2∙2∙2∙2∙2
33 = 3∙11
34 = 2∙17
35 = 5∙7
36 = 2∙2∙3∙3
37 = [prime] 37
38 = 2∙19
39 = 3∙13
40 = 2∙2∙2∙5
12 primes found.
Using REXX libraries
Libraries: How to use
Library: Numbers
Library: Functions
Library: Sequences
The factorization procedure Factors() is in library Sequences, returning the factor count and the factors itself in fact.factor.1, fact.factor.2 and so on.
call Time('r')
say 'Count in factors - Using REXX libraries'
parse version version; say version
say
numeric digits 16
call CountFactors 1,20
call CountFactors 1e3,1e3+20
call CountFactors 1e6,1e6+20
call CountFactors 1e9,1e9+20
call CountFactors 1e12,1e12+20
call CountFactors 1e15,1e15+20
say Format(Time('e'),,3) 'seconds'
exit
CountFactors:
arg x,y
say 'Factorization of the numbers' x 'to' y
say
do i = x to y
f = Factors(i)
if i = 1 then
s = '1 = 1'
else
s = i '='
do j = 1 to f
s = s fact.factor.j
if j < f then
s = s 'x'
end
say s
end
say
return
include Numbers
include Sequences
include Functions
- Output:
Count in factors - Using REXX libraries REXX-ooRexx_5.0.0(MT)_64-bit 6.05 23 Dec 2022 Factorization of the numbers 1 to 20 1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5 Factorization of the numbers 1E3 to 1020 1000 = 2 x 2 x 2 x 5 x 5 x 5 1001 = 7 x 11 x 13 1002 = 2 x 3 x 167 1003 = 17 x 59 1004 = 2 x 2 x 251 1005 = 3 x 5 x 67 1006 = 2 x 503 1007 = 19 x 53 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7 1009 = 1009 1010 = 2 x 5 x 101 1011 = 3 x 337 1012 = 2 x 2 x 11 x 23 1013 = 1013 1014 = 2 x 3 x 13 x 13 1015 = 5 x 7 x 29 1016 = 2 x 2 x 2 x 127 1017 = 3 x 3 x 113 1018 = 2 x 509 1019 = 1019 1020 = 2 x 2 x 3 x 5 x 17 Factorization of the numbers 1E6 to 1000020 1000000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 1000001 = 101 x 9901 1000002 = 2 x 3 x 166667 1000003 = 1000003 1000004 = 2 x 2 x 53 x 53 x 89 1000005 = 3 x 5 x 163 x 409 1000006 = 2 x 7 x 71429 1000007 = 29 x 34483 1000008 = 2 x 2 x 2 x 3 x 3 x 17 x 19 x 43 1000009 = 293 x 3413 1000010 = 2 x 5 x 11 x 9091 1000011 = 3 x 333337 1000012 = 2 x 2 x 13 x 19231 1000013 = 7 x 373 x 383 1000014 = 2 x 3 x 166669 1000015 = 5 x 200003 1000016 = 2 x 2 x 2 x 2 x 62501 1000017 = 3 x 3 x 23 x 4831 1000018 = 2 x 500009 1000019 = 47 x 21277 1000020 = 2 x 2 x 3 x 5 x 7 x 2381 Factorization of the numbers 1E9 to 1000000020 1000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 1000000001 = 7 x 11 x 13 x 19 x 52579 1000000002 = 2 x 3 x 43 x 983 x 3943 1000000003 = 23 x 307 x 141623 1000000004 = 2 x 2 x 41 x 41 x 148721 1000000005 = 3 x 5 x 66666667 1000000006 = 2 x 500000003 1000000007 = 1000000007 1000000008 = 2 x 2 x 2 x 3 x 3 x 7 x 109 x 109 x 167 1000000009 = 1000000009 1000000010 = 2 x 5 x 17 x 5882353 1000000011 = 3 x 29 x 11494253 1000000012 = 2 x 2 x 11 x 47 x 79 x 6121 1000000013 = 7699 x 129887 1000000014 = 2 x 3 x 13 x 103 x 124471 1000000015 = 5 x 7 x 31 x 223 x 4133 1000000016 = 2 x 2 x 2 x 2 x 62500001 1000000017 = 3 x 3 x 111111113 1000000018 = 2 x 500000009 1000000019 = 83 x 12048193 1000000020 = 2 x 2 x 3 x 5 x 19 x 739 x 1187 Factorization of the numbers 1E12 to 1000000000020 1000000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 1000000000001 = 73 x 137 x 99990001 1000000000002 = 2 x 3 x 166666666667 1000000000003 = 61 x 14221 x 1152763 1000000000004 = 2 x 2 x 17 x 149 x 197 x 501001 1000000000005 = 3 x 5 x 66666666667 1000000000006 = 2 x 7 x 607 x 117674747 1000000000007 = 34519 x 28969553 1000000000008 = 2 x 2 x 2 x 3 x 3 x 1667 x 8331667 1000000000009 = 29 x 66413 x 519217 1000000000010 = 2 x 5 x 11 x 11 x 23 x 4093 x 8779 1000000000011 = 3 x 269 x 5107 x 242639 1000000000012 = 2 x 2 x 13 x 19 x 1012145749 1000000000013 = 7 x 142857142859 1000000000014 = 2 x 3 x 166666666669 1000000000015 = 5 x 47 x 1171 x 3633919 1000000000016 = 2 x 2 x 2 x 2 x 13177 x 4743113 1000000000017 = 3 x 3 x 461 x 241021933 1000000000018 = 2 x 39041 x 12807049 1000000000019 = 1601 x 2593 x 240883 1000000000020 = 2 x 2 x 3 x 5 x 7 x 1543 x 1543067 Factorization of the numbers 1E15 to 1000000000000020 1000000000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 1000000000000001 = 7 x 11 x 13 x 211 x 241 x 2161 x 9091 1000000000000002 = 2 x 3 x 166666666666667 1000000000000003 = 14902357 x 67103479 1000000000000004 = 2 x 2 x 648931 x 385248971 1000000000000005 = 3 x 5 x 17 x 1873 x 41161 x 50867 1000000000000006 = 2 x 53 x 349 x 27031410499 1000000000000007 = 47 x 59 x 360620266859 1000000000000008 = 2 x 2 x 2 x 3 x 3 x 7 x 2381 x 833316667 1000000000000009 = 179 x 367 x 47207 x 322459 1000000000000010 = 2 x 5 x 29 x 101 x 281 x 121499449 1000000000000011 = 3 x 19 x 61 x 176651 x 1628093 1000000000000012 = 2 x 2 x 11 x 113 x 201126307321 1000000000000013 = 1091 x 916590284143 1000000000000014 = 2 x 3 x 13 x 5749 x 2230042237 1000000000000015 = 5 x 7 x 8431 x 3388854059 1000000000000016 = 2 x 2 x 2 x 2 x 62500000000001 1000000000000017 = 3 x 3 x 1163 x 95538358651 1000000000000018 = 2 x 23 x 23 x 23 x 3221 x 12758387 1000000000000019 = 1151 x 868809730669 1000000000000020 = 2 x 2 x 3 x 5 x 89 x 251 x 746079353 5.139 seconds
Ring
for i = 1 to 20
see "" + i + " = " + factors(i) + nl
next
func factors n
f = ""
if n = 1 return "1" ok
p = 2
while p <= n
if (n % p) = 0
f += string(p) + " x "
n = n/p
else p += 1 ok
end
return left(f, len(f) - 3)Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5
RPL
PDIV is defined at Prime decomposition
≪ { "1" } 2 ROT FOR j
"" j PDIV → factors
≪ IF factors SIZE 1 == THEN j →STR +
ELSE
1 factors SIZE FOR k
IF k 1 ≠ THEN 130 CHR + END
factors k GET →STR +
NEXT END
≫ + NEXT
≫ 'TASK' STO
20 TASK
- Output:
1: { "1" "2" "3" "2×2" "5" "2×3" "7" "2×2×2" "3×3" "2×5" "11" "2×2×3" "13" "2×7" "3×5" "2×2×2×2" "17" "2×3×3" "19" "2×2×5" }
Ruby
Starting with Ruby 1.9, 'prime' is part of the standard library and provides Integer#prime_division.
require 'optparse'
require 'prime'
maximum = 10
OptionParser.new do |o|
o.banner = "Usage: #{File.basename $0} [-m MAXIMUM]"
o.on("-m MAXIMUM", Integer,
"Count up to MAXIMUM [#{maximum}]") { |m| maximum = m }
o.parse! rescue ($stderr.puts $!, o; exit 1)
($stderr.puts o; exit 1) unless ARGV.size == 0
end
# 1 has no prime factors
puts "1 is 1" unless maximum < 1
2.upto(maximum) do |i|
# i is 504 => i.prime_division is [[2, 3], [3, 2], [7, 1]]
f = i.prime_division.map! do |factor, exponent|
# convert [2, 3] to "2 x 2 x 2"
([factor] * exponent).join " x "
end.join " x "
puts "#{i} is #{f}"
end
- Example:
$ ruby prime-count.rb -h
Usage: prime-count.rb [-m MAXIMUM]
-m MAXIMUM Count up to MAXIMUM [10]
$ ruby prime-count.rb -m 10000 | sed -e '11,9990d'
1 is 1
2 is 2
3 is 3
4 is 2 x 2
5 is 5
6 is 2 x 3
7 is 7
8 is 2 x 2 x 2
9 is 3 x 3
10 is 2 x 5
9991 is 97 x 103
9992 is 2 x 2 x 2 x 1249
9993 is 3 x 3331
9994 is 2 x 19 x 263
9995 is 5 x 1999
9996 is 2 x 2 x 3 x 7 x 7 x 17
9997 is 13 x 769
9998 is 2 x 4999
9999 is 3 x 3 x 11 x 101
10000 is 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
Run BASIC
for i = 1000 to 1016
print i;" = "; factorial$(i)
next
wait
function factorial$(num)
if num = 1 then factorial$ = "1"
fct = 2
while fct <= num
if (num mod fct) = 0 then
factorial$ = factorial$ ; x$ ; fct
x$ = " x "
num = num / fct
else
fct = fct + 1
end if
wend
end function- Output:
1000 = 2 x 2 x 2 x 5 x 5 x 5 1001 = 7 x 11 x 13 1002 = 2 x 3 x 167 1003 = 17 x 59 1004 = 2 x 2 x 251 1005 = 3 x 5 x 67 1006 = 2 x 503 1007 = 19 x 53 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7 1009 = 1009 1010 = 2 x 5 x 101 1011 = 3 x 337 1012 = 2 x 2 x 11 x 23 1013 = 1013 1014 = 2 x 3 x 13 x 13 1015 = 5 x 7 x 29 1016 = 2 x 2 x 2 x 127
Rust
You can run and experiment with this code at https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=b66c14d944ff0472d2460796513929e2
use std::env;
fn main() {
let args: Vec<_> = env::args().collect();
let n = if args.len() > 1 {
args[1].parse().expect("Not a valid number to count to")
}
else {
20
};
count_in_factors_to(n);
}
fn count_in_factors_to(n: u64) {
println!("1");
let mut primes = vec![];
for i in 2..=n {
let fs = factors(&primes, i);
if fs.len() <= 1 {
primes.push(i);
println!("{}", i);
}
else {
println!("{} = {}", i, fs.iter().map(|f| f.to_string()).collect::<Vec<String>>().join(" x "));
}
}
}
fn factors(primes: &[u64], mut n: u64) -> Vec<u64> {
let mut result = Vec::new();
for p in primes {
while n % p == 0 {
result.push(*p);
n /= p;
}
if n == 1 {
return result;
}
}
vec![n]
}
- Output:
1 2 3 4 = 2 x 2 5 6 = 2 x 3 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 12 = 2 x 2 x 3 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 18 = 2 x 3 x 3 19 20 = 2 x 2 x 5
Sage
def count_in_factors(n):
if is_prime(n) or n == 1:
print(n,end="")
return
while n != 1:
p = next_prime(1)
while n % p != 0:
p = next_prime(p)
print(p,end="")
n = n / p
if n != 1: print(" x",end=" ")
for i in range(1, 101):
print(i,"=",end=" ")
count_in_factors(i)
print("")
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5 21 = 3 x 7 22 = 2 x 11 23 = 23 24 = 2 x 2 x 2 x 3 25 = 5 x 5 26 = 2 x 13 27 = 3 x 3 x 3 28 = 2 x 2 x 7 29 = 29 30 = 2 x 3 x 5 31 = 31 32 = 2 x 2 x 2 x 2 x 2 33 = 3 x 11 34 = 2 x 17 35 = 5 x 7 36 = 2 x 2 x 3 x 3 37 = 37 38 = 2 x 19 39 = 3 x 13 40 = 2 x 2 x 2 x 5 41 = 41 ... 85 = 5 x 17 86 = 2 x 43 87 = 3 x 29 88 = 2 x 2 x 2 x 11 89 = 89 90 = 2 x 3 x 3 x 5 91 = 7 x 13 92 = 2 x 2 x 23 93 = 3 x 31 94 = 2 x 47 95 = 5 x 19 96 = 2 x 2 x 2 x 2 x 2 x 3 97 = 97 98 = 2 x 7 x 7 99 = 3 x 3 x 11 100 = 2 x 2 x 5 x 5
Scala
object CountInFactors extends App {
def primeFactors(n: Int): List[Int] = {
def primeStream(s: LazyList[Int]): LazyList[Int] = {
s.head #:: primeStream(s.tail filter {
_ % s.head != 0
})
}
val primes = primeStream(LazyList.from(2))
def factors(n: Int): List[Int] = primes.takeWhile(_ <= n).find(n % _ == 0) match {
case None => Nil
case Some(p) => p :: factors(n / p)
}
if (n == 1) List(1) else factors(n)
}
// A little test...
{
val nums = (1 to 12).toList :+ 2144 :+ 6358
nums.foreach(n => println("%6d : %s".format(n, primeFactors(n).mkString(" * "))))
}
}
- 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
2144 : 2 * 2 * 2 * 2 * 2 * 67
6358 : 2 * 11 * 17 * 17
Scheme
(define (factors n)
(let facs ((l '()) (d 2) (x n))
(cond ((= x 1) (if (null? l) '(1) l))
((< x (* d d)) (cons x l))
(else (if (= 0 (modulo x d))
(facs (cons d l) d (/ x d))
(facs l (+ 1 d) x))))))
(define (show l)
(display (car l))
(if (not (null? (cdr l)))
(begin
(display " × ")
(show (cdr l)))
(display "\n")))
(do ((i 1 (+ i 1))) (#f)
(display i)
(display " = ")
(show (reverse (factors i))))
- 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 ...
Seed7
$ include "seed7_05.s7i";
const proc: writePrimeFactors (in var integer: number) is func
local
var boolean: laterElement is FALSE;
var integer: checker is 2;
begin
while checker * checker <= number do
if number rem checker = 0 then
if laterElement then
write(" * ");
end if;
laterElement := TRUE;
write(checker);
number := number div checker;
else
incr(checker);
end if;
end while;
if number <> 1 then
if laterElement then
write(" * ");
end if;
laterElement := TRUE;
write(number);
end if;
end func;
const proc: main is func
local
var integer: number is 0;
begin
writeln("1: 1");
for number range 2 to 2147483647 do
write(number <& ": ");
writePrimeFactors(number);
writeln;
end for;
end func;- 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 . . .
Sidef
class Counter {
method factors(n, p=2) {
var a = gather {
while (n >= p*p) {
while (p `divides` n) {
take(p)
n //= p
}
p = self.next_prime(p)
}
}
(n > 1 || a.is_empty) ? (a << n) : a
}
method is_prime(n) {
self.factors(n).len == 1
}
method next_prime(p) {
do {
p == 2 ? (p = 3) : (p+=2)
} while (!self.is_prime(p))
return p
}
}
for i in (1..100) {
say "#{i} = #{Counter().factors(i).join(' × ')}"
}
Swift
extension BinaryInteger {
@inlinable
public func primeDecomposition() -> [Self] {
guard self > 1 else { return [] }
func step(_ x: Self) -> Self {
return 1 + (x << 2) - ((x >> 1) << 1)
}
let maxQ = Self(Double(self).squareRoot())
var d: Self = 1
var q: Self = self & 1 == 0 ? 2 : 3
while q <= maxQ && self % q != 0 {
q = step(d)
d += 1
}
return q <= maxQ ? [q] + (self / q).primeDecomposition() : [self]
}
}
for i in 1...20 {
if i == 1 {
print("1 = 1")
} else {
print("\(i) = \(i.primeDecomposition().map(String.init).joined(separator: " x "))")
}
}
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 11 = 11 12 = 2 x 2 x 3 13 = 13 14 = 2 x 7 15 = 3 x 5 16 = 2 x 2 x 2 x 2 17 = 17 18 = 2 x 3 x 3 19 = 19 20 = 2 x 2 x 5
Tcl
This factorization code is based on the same engine that is used in the parallel computation task.
package require Tcl 8.5
namespace eval prime {
variable primes [list 2 3 5 7 11]
proc restart {} {
variable index -1
variable primes
variable current [lindex $primes end]
}
proc get_next_prime {} {
variable primes
variable index
if {$index < [llength $primes]-1} {
return [lindex $primes [incr index]]
}
variable current
while 1 {
incr current 2
set p 1
foreach prime $primes {
if {$current % $prime} {} else {
set p 0
break
}
}
if {$p} {
return [lindex [lappend primes $current] [incr index]]
}
}
}
proc factors {num} {
restart
set factors [dict create]
for {set i [get_next_prime]} {$i <= $num} {} {
if {$num % $i == 0} {
dict incr factors $i
set num [expr {$num / $i}]
continue
} elseif {$i*$i > $num} {
dict incr factors $num
break
} else {
set i [get_next_prime]
}
}
return $factors
}
# Produce the factors in rendered form
proc factors.rendered {num} {
set factorDict [factors $num]
if {[dict size $factorDict] == 0} {
return 1
}
dict for {factor times} $factorDict {
lappend v {*}[lrepeat $times $factor]
}
return [join $v "*"]
}
}
Demonstration code:
set max 20
for {set i 1} {$i <= $max} {incr i} {
puts [format "%*d = %s" [string length $max] $i [prime::factors.rendered $i]]
}
VBScript
Made minor modifications on the code I posted under Prime Decomposition.
Function CountFactors(n)
If n = 1 Then
CountFactors = 1
Else
arrP = Split(ListPrimes(n)," ")
Set arrList = CreateObject("System.Collections.ArrayList")
divnum = n
Do Until divnum = 1
'The -1 is to account for the null element of arrP
For i = 0 To UBound(arrP)-1
If divnum = 1 Then
Exit For
ElseIf divnum Mod arrP(i) = 0 Then
divnum = divnum/arrP(i)
arrList.Add arrP(i)
End If
Next
Loop
arrList.Sort
For i = 0 To arrList.Count - 1
If i = arrList.Count - 1 Then
CountFactors = CountFactors & arrList(i)
Else
CountFactors = CountFactors & arrList(i) & " * "
End If
Next
End If
End Function
Function IsPrime(n)
If n = 2 Then
IsPrime = True
ElseIf n <= 1 Or n Mod 2 = 0 Then
IsPrime = False
Else
IsPrime = True
For i = 3 To Int(Sqr(n)) Step 2
If n Mod i = 0 Then
IsPrime = False
Exit For
End If
Next
End If
End Function
Function ListPrimes(n)
ListPrimes = ""
For i = 1 To n
If IsPrime(i) Then
ListPrimes = ListPrimes & i & " "
End If
Next
End Function
'Testing the fucntions.
WScript.StdOut.Write "2 = " & CountFactors(2)
WScript.StdOut.WriteLine
WScript.StdOut.Write "2144 = " & CountFactors(2144)
WScript.StdOut.WriteLine
- Output:
2 = 2 2144 = 2 * 2 * 2 * 2 * 2 * 67
Visual Basic .NET
Module CountingInFactors
Sub Main()
For i As Integer = 1 To 10
Console.WriteLine("{0} = {1}", i, CountingInFactors(i))
Next
For i As Integer = 9991 To 10000
Console.WriteLine("{0} = {1}", i, CountingInFactors(i))
Next
End Sub
Private Function CountingInFactors(ByVal n As Integer) As String
If n = 1 Then Return "1"
Dim sb As New Text.StringBuilder()
CheckFactor(2, n, sb)
If n = 1 Then Return sb.ToString()
CheckFactor(3, n, sb)
If n = 1 Then Return sb.ToString()
For i As Integer = 5 To n Step 2
If i Mod 3 = 0 Then Continue For
CheckFactor(i, n, sb)
If n = 1 Then Exit For
Next
Return sb.ToString()
End Function
Private Sub CheckFactor(ByVal mult As Integer, ByRef n As Integer, ByRef sb As Text.StringBuilder)
Do While n Mod mult = 0
If sb.Length > 0 Then sb.Append(" x ")
sb.Append(mult)
n = n / mult
Loop
End Sub
End Module
- Output:
1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 9 = 3 x 3 10 = 2 x 5 9991 = 97 x 103 9992 = 2 x 2 x 2 x 1249 9993 = 3 x 3331 9994 = 2 x 19 x 263 9995 = 5 x 1999 9996 = 2 x 2 x 3 x 7 x 7 x 17 9997 = 13 x 769 9998 = 2 x 4999 9999 = 3 x 3 x 11 x 101 10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
V (Vlang)
fn main() {
println("1: 1")
for i := 2; ; i++ {
print("$i: ")
mut x := ''
for n, f := i, 2; n != 1; f++ {
for m := n % f; m == 0; m = n % f {
print('$x$f')
x = "×"
n /= f
}
}
println('')
}
}- 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 ...
Wren
import "./math" for Int
for (r in [1..9, 2144..2154, 9987..9999]) {
for (i in r) {
var factors = (i > 1) ? Int.primeFactors(i) : [1]
System.print("%(i): %(factors.join(" x "))")
}
System.print()
}
- Output:
1: 1 2: 2 3: 3 4: 2 x 2 5: 5 6: 2 x 3 7: 7 8: 2 x 2 x 2 9: 3 x 3 2144: 2 x 2 x 2 x 2 x 2 x 67 2145: 3 x 5 x 11 x 13 2146: 2 x 29 x 37 2147: 19 x 113 2148: 2 x 2 x 3 x 179 2149: 7 x 307 2150: 2 x 5 x 5 x 43 2151: 3 x 3 x 239 2152: 2 x 2 x 2 x 269 2153: 2153 2154: 2 x 3 x 359 9987: 3 x 3329 9988: 2 x 2 x 11 x 227 9989: 7 x 1427 9990: 2 x 3 x 3 x 3 x 5 x 37 9991: 97 x 103 9992: 2 x 2 x 2 x 1249 9993: 3 x 3331 9994: 2 x 19 x 263 9995: 5 x 1999 9996: 2 x 2 x 3 x 7 x 7 x 17 9997: 13 x 769 9998: 2 x 4999 9999: 3 x 3 x 11 x 101
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;
]Example 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
foreach n in ([1..*]){ println(n,": ",primeFactors(n).concat("\U2715;")) }Using the fixed size integer (64 bit) solution from Prime decomposition#zkl
fcn primeFactors(n){ // Return a list of factors of n
acc:=fcn(n,k,acc,maxD){ // k is 2,3,5,7,9,... not optimum
if(n==1 or k>maxD) acc.close();
else{
q,r:=n.divr(k); // divr-->(quotient,remainder)
if(r==0) return(self.fcn(q,k,acc.write(k),q.toFloat().sqrt()));
return(self.fcn(n,k+1+k.isOdd,acc,maxD))
}
}(n,2,Sink(List),n.toFloat().sqrt());
m:=acc.reduce('*,1); // mulitply factors
if(n!=m) acc.append(n/m); // opps, missed last factor
else acc;
}- Output:
1: 2: 2 3: 3 4: 2✕2 5: 5 6: 2✕3 ... 591885: 3✕3✕5✕7✕1879 591886: 2✕295943 591887: 591887 591888: 2✕2✕2✕2✕3✕11✕19✕59 ...
ZX Spectrum Basic
10 FOR i=1 TO 20
20 PRINT i;" = ";
30 IF i=1 THEN PRINT 1: GO TO 90
40 LET p=2: LET n=i: LET f$=""
50 IF p>n THEN GO TO 80
60 IF NOT FN m(n,p) THEN LET f$=f$+STR$ p+" x ": LET n=INT (n/p): GO TO 50
70 LET p=p+1: GO TO 50
80 PRINT f$( TO LEN f$-3)
90 NEXT i
100 STOP
110 DEF FN m(a,b)=a-INT (a/b)*b
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