# Count in factors

Count in factors
You are encouraged to solve this task according to the task description, using any language you may know.

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   ${\displaystyle 2\times 3}$.
2144   is not prime;   it would be shown as   ${\displaystyle 2\times 2\times 2\times 2\times 2\times 67}$.

## 11l

Translation of: C++
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:
1=1
2=2
3=3
4=2x2
5=5
...
995=5x199
996=2x2x3x83
997=997
998=2x499
999=3x3x3x37
1000=2x2x2x5x5x5


The solution uses the generic package Prime_Numbers from Prime decomposition#Ada

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
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));
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

Translation of: Euphoria
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

Works with: as version Raspberry Pi
/* 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
bl conversion10               @ call décimal conversion
ldr r1,iAdrsZoneConv          @ insert conversion in message
bl strInsertAtCharInc
bl affichageMess              @ display message
mov r0,r7
bl decompFact
cmp r0,#-1
beq 98f                       @ error ?
mov r1,r0
bl displayDivisors

b 100f
98:
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
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:
ldr r7,[r5]                 @ load factor
ldr r6,[r5,#4]              @ load number of factor
mov r8,#0                   @ display factor counter
2:
mov r0,r7
bl conversion10             @ call décimal conversion
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
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
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
str r7,[r5,r4,lsl #2]      @ and store last number of same divisors
lsr r0,r4,#1               @ return number of table items
mov r3,#0
str r3,[r5,r4,lsl #2]      @ store zéro in last table item
str r3,[r5,r4,lsl #2]      @ and zero in counter same divisor
b 100f

98:
bl   affichageMess
mov r0,#1                   @ return code
b 100f
99:
bl   affichageMess
mov r0,#-1                  @ error code
b 100f
100:
pop {r1-r8,lr}              @ restaur registers
bx lr

/***************************************************/
/*   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
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

Translation of: D
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  RETURN

### BASIC256

Translation of: Run BASIC
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

Works with: Chipmunk Basic version 3.6.4
Translation of: Run 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

Translation of: Run 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

Translation of: Run BASIC
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 )
{
}
else
{
int k = 2;
while( n > 1 )
{
while( n % k == 0 )
{
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

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

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

procedure main()
write("Press ^C to terminate")
every f := [i:= 1] | factors(i := seq(2)) do {
writes(i," : [")
every writes(" ",!f|"]\n")
}
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 ]
...

## 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

Translation of: Visual Basic .NET
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: 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_factors

## M4

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

Translation of: Java
/* 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

Translation of: C
var primes = newSeq[int]()

proc getPrime(idx: int): int =
if idx >= primes.len:
if primes.len == 0:

var last = primes[primes.high]
while idx >= primes.len:
last += 2
for i, p in primes:
if p * p > 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

Works with: Free_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:

Library: ntheory
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
Factors() = 2
Number / 2
Wend
Max = Number
While I <= Max And Number > 1
While Number % I = 0
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) Works with: rakudo version 2015-10-01 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

The factorization procedure Factors() is in library Numbers, 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 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

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)
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)

Translation of: go
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 Library: Wren-math 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 Translation of: BBC_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