Count in factors

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

Write a program which counts up from   1,   displaying each number as the multiplication of its prime factors.

For the purpose of this task,   1   (unity)   may be shown as itself.


Example

      2   is prime,   so it would be shown as itself.
      6   is not prime;   it would be shown as   .
2144   is not prime;   it would be shown as   .


Related tasks



11l[edit]

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[edit]

*        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![edit]

PROC PrintFactors(CARD a)
  BYTE notFirst
  CARD p

  IF a=1 THEN
    PrintC(a) RETURN
  FI

  p=2 notFirst=0
  WHILE p<=a
  DO
    IF a MOD p=0 THEN
      IF notFirst THEN
        Put('x)
      FI
      notFirst=1
      PrintC(p)
      a==/p
    ELSE
      p==+1
    FI
  OD
RETURN

PROC Main()
  CARD i

  FOR i=1 TO 1000
  DO
    PrintC(i) Put('=)
    PrintFactors(i)
    PutE()
  OD
RETURN
Output:

Screenshot from Atari 8-bit computer

1=1
2=2
3=3
4=2x2
5=5
...
995=5x199
996=2x2x3x83
997=997
998=2x499
999=3x3x3x37
1000=2x2x2x5x5x5

Ada[edit]

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

count.adb
with Ada.Command_Line, Ada.Text_IO, Prime_Numbers;
 
procedure Count is
   package Prime_Nums is new Prime_Numbers
     (Number => Natural, Zero => 0, One => 1, Two => 2); use Prime_Nums;
 
   procedure Put (List : Number_List) is
   begin
      for Index in List'Range loop
         Ada.Text_IO.Put (Integer'Image (List (Index)));
         if Index /= List'Last then
            Ada.Text_IO.Put (" x");
         end if;
      end loop;
   end Put;
 
   N     : Natural := 1;
   Max_N : Natural := 15; -- the default for Max_N
begin
   if Ada.Command_Line.Argument_Count = 1 then -- read Max_N from command line
      Max_N := Integer'Value (Ada.Command_Line.Argument (1));
   end if; -- else use the default
   loop
      Ada.Text_IO.Put (Integer'Image (N) & ": ");
      Put (Decompose (N));
      Ada.Text_IO.New_Line;
      N := N + 1;
      exit when N > Max_N;
   end loop;
end Count;
Output:
 1:  1
 2:  2
 3:  3
 4:  2 x 2
 5:  5
 6:  2 x 3
 7:  7
 8:  2 x 2 x 2
 9:  3 x 3
 10:  2 x 5
 11:  11
 12:  2 x 2 x 3
 13:  13
 14:  2 x 7
 15:  3 x 5

ALGOL 68[edit]

Translation of: Euphoria
OP +:= = (REF FLEX []INT a, INT b) VOID:
   BEGIN
      [⌈a + 1] INT c;
      c[:⌈a] := a;
      c[⌈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

ARM Assembly[edit]

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
    ldr r1,iAdrsZoneConv
    bl conversion10               @ call décimal conversion
    ldr r0,iAdrszMessNumber
    ldr r1,iAdrsZoneConv          @ insert conversion in message
    bl strInsertAtCharInc
    bl affichageMess              @ display message
    mov r0,r7
    ldr r1,iAdrtbZoneDecom
    bl decompFact
    cmp r0,#-1
    beq 98f                       @ error ?
    mov r1,r0
    ldr r0,iAdrtbZoneDecom
    bl displayDivisors

    b 100f
98:
    ldr r0,iAdrszErrorGen
    bl affichageMess 
100:                              @ standard end of the program 
    mov r0, #0                    @ return code
    mov r7, #EXIT                 @ request to exit program
    svc #0                        @ perform the system call
iAdrszCarriageReturn:    .int szCarriageReturn
iAdrszMessResultFact:    .int szMessResultFact
iAdrszErrorGen:          .int szErrorGen
iAdrsZoneConv:           .int sZoneConv  
iAdrtbZoneDecom:         .int tbZoneDecom
iAdrszMessNumber:        .int szMessNumber
iNombre:                 .int NOMBRE
/******************************************************************/
/*     display divisors function                         */ 
/******************************************************************/
/* r0 contains address of divisors area */
/* r1 contains the number of area items  */
displayDivisors:
    push {r2-r8,lr}            @ save  registers 
    cmp r1,#0
    beq 100f
    mov r2,r1
    mov r3,#0                   @ indice
    mov r4,r0
1:
    add r5,r4,r3,lsl #3
    ldr r7,[r5]                 @ load factor
    ldr r6,[r5,#4]              @ load number of factor
    mov r8,#0                   @ display factor counter
2:
    mov r0,r7
    ldr r1,iAdrsZoneConv
    bl conversion10             @ call décimal conversion
    ldr r0,iAdrszMessResultFact
    ldr r1,iAdrsZoneConv        @ insert conversion in message
    bl strInsertAtCharInc
    bl affichageMess            @ display message
    add r8,#1                   @ increment counter
    cmp r8,r6                   @ same factors number ?
    blt 2b
    add r3,#1                   @ other ithem
    cmp r3,r2                   @ items maxi ?
    blt 1b
    ldr r0,iAdrszCarriageReturn
    bl affichageMess 
    b 100f

100:
    pop {r2-r8,lr}             @ restaur registers
    bx lr                       @ return
/******************************************************************/
/*     factor decomposition                                               */ 
/******************************************************************/
/* r0 contains number */
/* r1 contains address of divisors area */
/* r0 return divisors items in table */
decompFact:
    push {r1-r8,lr}            @ save  registers
    mov r5,r1
    mov r8,r0                  @ save number
    bl isPrime                 @ prime ?
    cmp r0,#1
    beq 98f                    @ yes is prime
    mov r4,#0                  @ raz indice
    mov r1,#2                  @ first divisor
    mov r6,#0                  @ previous divisor
    mov r7,#0                  @ number of same divisors
2:
    mov r0,r8                  @ dividende
    bl division                @  r1 divisor r2 quotient r3 remainder
    cmp r3,#0
    bne 5f                     @ if remainder <> zero  -> no divisor
    mov r8,r2                  @ else quotient -> new dividende
    cmp r1,r6                  @ same divisor ?
    beq 4f                     @ yes
    cmp r6,#0                  @ no but is the first divisor ?
    beq 3f                     @ yes 
    str r6,[r5,r4,lsl #2]      @ else store in the table
    add r4,r4,#1               @ and increment counter
    str r7,[r5,r4,lsl #2]      @ store counter
    add r4,r4,#1               @ next item
    mov r7,#0                  @ and raz counter
3:
    mov r6,r1                  @ new divisor
4:
    add r7,r7,#1               @ increment counter
    b 7f                       @ and loop
    
    /* not divisor -> increment next divisor */
5:
    cmp r1,#2                  @ if divisor = 2 -> add 1 
    addeq r1,#1
    addne r1,#2                @ else add 2
    b 2b
    
    /* divisor -> test if new dividende is prime */
7: 
    mov r3,r1                  @ save divisor
    cmp r8,#1                  @ dividende = 1 ? -> end
    beq 10f
    mov r0,r8                  @ new dividende is prime ?
    mov r1,#0
    bl isPrime                 @ the new dividende is prime ?
    cmp r0,#1
    bne 10f                    @ the new dividende is not prime

    cmp r8,r6                  @ else dividende is same divisor ?
    beq 9f                     @ yes
    cmp r6,#0                  @ no but is the first divisor ?
    beq 8f                     @ yes it is a first
    str r6,[r5,r4,lsl #2]      @ else store in table
    add r4,r4,#1               @ and increment counter
    str r7,[r5,r4,lsl #2]      @ and store counter 
    add r4,r4,#1               @ next item
8:
    mov r6,r8                  @ new dividende -> divisor prec
    mov r7,#0                  @ and raz counter
9:
    add r7,r7,#1               @ increment counter
    b 11f
    
10:
    mov r1,r3                  @ current divisor = new divisor
    cmp r1,r8                  @ current divisor  > new dividende ?
    ble 2b                     @ no -> loop
    
    /* end decomposition */ 
11:
    str r6,[r5,r4,lsl #2]      @ store last divisor
    add r4,r4,#1
    str r7,[r5,r4,lsl #2]      @ and store last number of same divisors
    add r4,r4,#1
    lsr r0,r4,#1               @ return number of table items
    mov r3,#0
    str r3,[r5,r4,lsl #2]      @ store zéro in last table item
    add r4,r4,#1
    str r3,[r5,r4,lsl #2]      @ and zero in counter same divisor
    b 100f

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

/***************************************************/
/*   check if a number is prime              */
/***************************************************/
/* r0 contains the number            */
/* r0 return 1 if prime  0 else */
@2147483647
@4294967297
@131071
isPrime:
    push {r1-r6,lr}    @ save registers 
    cmp r0,#0
    beq 90f
    cmp r0,#17
    bhi 1f
    cmp r0,#3
    bls 80f            @ for 1,2,3 return prime
    cmp r0,#5
    beq 80f            @ for 5 return prime
    cmp r0,#7
    beq 80f            @ for 7 return prime
    cmp r0,#11
    beq 80f            @ for 11 return prime
    cmp r0,#13
    beq 80f            @ for 13 return prime
    cmp r0,#17
    beq 80f            @ for 17 return prime
1:
    tst r0,#1          @ even ?
    beq 90f            @ yes -> not prime
    mov r2,r0          @ save number
    sub r1,r0,#1       @ exposant n - 1
    mov r0,#3          @ base
    bl moduloPuR32     @ compute base power n - 1 modulo n
    cmp r0,#1
    bne 90f            @ if <> 1  -> not prime
 
    mov r0,#5
    bl moduloPuR32
    cmp r0,#1
    bne 90f
    
    mov r0,#7
    bl moduloPuR32
    cmp r0,#1
    bne 90f
    
    mov r0,#11
    bl moduloPuR32
    cmp r0,#1
    bne 90f
    
    mov r0,#13
    bl moduloPuR32
    cmp r0,#1
    bne 90f
    
    mov r0,#17
    bl moduloPuR32
    cmp r0,#1
    bne 90f
80:
    mov r0,#1        @ is prime
    b 100f
90:
    mov r0,#0        @ no prime
100:                 @ fin standard de la fonction 
    pop {r1-r6,lr}   @ restaur des registres
    bx lr            @ retour de la fonction en utilisant lr 
/********************************************************/
/*   Calcul modulo de b puissance e modulo m  */
/*    Exemple 4 puissance 13 modulo 497 = 445         */
/*                                             */
/********************************************************/
/* r0  nombre  */
/* r1 exposant */
/* r2 modulo   */
/* r0 return result  */
moduloPuR32:
    push {r1-r7,lr}    @ save registers  
    cmp r0,#0          @ verif <> zero 
    beq 100f
    cmp r2,#0          @ verif <> zero 
    beq 100f           @ 
1:
    mov r4,r2          @ save modulo
    mov r5,r1          @ save exposant 
    mov r6,r0          @ save base
    mov r3,#1          @ start result

    mov r1,#0          @ division de r0,r1 par r2
    bl division32R
    mov r6,r2          @ base <- remainder
2:
    tst r5,#1          @  exposant even or odd
    beq 3f
    umull r0,r1,r6,r3
    mov r2,r4
    bl division32R
    mov r3,r2          @ result <- remainder
3:
    umull r0,r1,r6,r6
    mov r2,r4
    bl division32R
    mov r6,r2          @ base <- remainder

    lsr r5,#1          @ left shift 1 bit
    cmp r5,#0          @ end ?
    bne 2b
    mov r0,r3
100:                   @ fin standard de la fonction
    pop {r1-r7,lr}     @ restaur des registres
    bx lr              @ retour de la fonction en utilisant lr    

/***************************************************/
/*   division number 64 bits in 2 registers by number 32 bits */
/***************************************************/
/* r0 contains lower part dividende   */
/* r1 contains upper part dividende   */
/* r2 contains divisor   */
/* r0 return lower part quotient    */
/* r1 return upper part quotient    */
/* r2 return remainder               */
division32R:
    push {r3-r9,lr}    @ save registers
    mov r6,#0          @ init upper upper part remainder  !!
    mov r7,r1          @ init upper part remainder with upper part dividende
    mov r8,r0          @ init lower part remainder with lower part dividende
    mov r9,#0          @ upper part quotient 
    mov r4,#0          @ lower part quotient
    mov r5,#32         @ bits number
1:                     @ begin loop
    lsl r6,#1          @ shift upper upper part remainder
    lsls r7,#1         @ shift upper  part remainder
    orrcs r6,#1        
    lsls r8,#1         @ shift lower  part remainder
    orrcs r7,#1
    lsls r4,#1         @ shift lower part quotient
    lsl r9,#1          @ shift upper part quotient
    orrcs r9,#1
                       @ divisor sustract  upper  part remainder
    subs r7,r2
    sbcs  r6,#0        @ and substract carry
    bmi 2f             @ négative ?
    
                       @ positive or equal
    orr r4,#1          @ 1 -> right bit quotient
    b 3f
2:                     @ negative 
    orr r4,#0          @ 0 -> right bit quotient
    adds r7,r2         @ and restaur remainder
    adc  r6,#0 
3:
    subs r5,#1         @ decrement bit size 
    bgt 1b             @ end ?
    mov r0,r4          @ lower part quotient
    mov r1,r9          @ upper part quotient
    mov r2,r7          @ remainder
100:                   @ function end
    pop {r3-r9,lr}     @ restaur registers
    bx lr  


/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"
Number 2144        : 2           2           2           2           2           67

Arturo[edit]

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[edit]

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[edit]

# 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[edit]

Applesoft BASIC[edit]

 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[edit]

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

True BASIC[edit]

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[edit]

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[edit]

      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[edit]

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[edit]

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#[edit]

using System;
using System.Collections.Generic;

namespace prog
{
	class MainClass
	{
		public static void Main (string[] args)
		{
			for( int i=1; i<=22; i++ )
			{				
				List<int> f = Factorize(i);
				Console.Write( i + ":  " + f[0] );
				for( int j=1; j<f.Count; j++ )
				{
					Console.Write( " * " + f[j] );
				}
				Console.WriteLine();
			}
		}
		
		public static List<int> Factorize( int n )
		{
			List<int> l = new List<int>();
		    
			if ( n == 1 )
			{
				l.Add(1);
			}
			else
			{
				int k = 2;
				while( n > 1 ) 
				{
					while( n % k == 0 )
					{
						l.Add( k );
						n /= k;
					}
					k++;
				}
			}			
			return l;
		}	
	}
}

C++[edit]

#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[edit]

(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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

See Pascal.

DWScript[edit]

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[edit]

func isPrime num . result$ .
   if num < 2
      result$ = "false"
      break 1
   .
   if num mod 2 = 0 and num > 2
      result$ = "false"
      break 1
   .
   for i = 3 to sqrt num
      if num mod i = 0
         result$ = "false"
         break 2
      .
   .
   result$ = "true"
.
func decompose num . primes[] .
   # If the number is prime, return the number itself
   call isPrime num result$
   if result$ = "true"
      primes[] &= num
      break 1
   .
   currentPrime = 2
   currentNum = num
   repeat
      if currentNum mod currentPrime = 0
         primes[] &= currentPrime
         currentNum = currentNum / currentPrime
      else
         repeat
            currentPrime += 1
            call isPrime currentPrime result$
            until result$ = "true"
         .
      .
      call isPrime currentNum result$
      until result$ = "true"
   .
   primes[] &= currentNum
.
# The number 30 can be changed if you want to
for i = 1 to 30
   if i = 1
      print "1: 1"
   else
      write i & ": "
      call 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[edit]

(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[edit]

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[edit]

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[edit]

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#[edit]

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[edit]

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[edit]

: .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[edit]

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[edit]

' 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[edit]

Frink's factoring routines work on arbitrarily-large integers.

i = 1
while true
{
    println[join[" x ", factorFlat[i]]]
    i = i + 1
}

FutureBasic[edit]

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[edit]

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, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

In this page you can see the program(s) related to this task and their results.

Go[edit]

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[edit]

def factors(number) {
    if (number == 1) {
        return [1]
    }
    def factors = []
    BigInteger value = number
    BigInteger possibleFactor = 2
    while (possibleFactor <= value) {
        if (value % possibleFactor == 0) {
            factors << possibleFactor
            value /= possibleFactor
        } else {
            possibleFactor++
        }
    }
    factors
}
Number.metaClass.factors = { factors(delegate) }

((1..10) + (6351..6359)).each { number ->
    println "$number = ${number.factors().join(' x ')}"
}
Output:
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
6351 = 3 x 29 x 73
6352 = 2 x 2 x 2 x 2 x 397
6353 = 6353
6354 = 2 x 3 x 3 x 353
6355 = 5 x 31 x 41
6356 = 2 x 2 x 7 x 227
6357 = 3 x 13 x 163
6358 = 2 x 11 x 17 x 17
6359 = 6359

Haskell[edit]

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[edit]

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

link factors

factors.icn provides factors

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

// 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[edit]

'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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

n = 2; 
While[n < 100, 
 Print[Row[Riffle[Flatten[Map[Apply[ConstantArray, #] &, FactorInteger[n]]],"*"]]]; 
 n++]

NetRexx[edit]

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[edit]

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

proc getPrime(idx: int): int =
  if idx >= primes.len:
    if primes.len == 0:
      primes.add 2
      primes.add 3

    var last = primes[primes.high]
    while idx >= primes.len:
      last += 2
      for i, p in primes:
        if p * p > last:
          primes.add last
          break
        if last mod p == 0:
          break

  return primes[idx]

for x in 1 ..< int32.high.int:
  stdout.write x, " = "
  var n = x
  var first = true

  for i in 0 ..< int32.high:
    let p = getPrime(i)
    while n mod p == 0:
      n = n div p
      if not first: stdout.write " x "
      first = false
      stdout.write p

    if n <= p * p:
      break

  if first > 0: echo n
  elif n > 1:   echo " x ", n
  else:         echo ""
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
...

Objeck[edit]

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[edit]

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[edit]

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[edit]

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++, print(fnice(n)))

Pascal[edit]

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

Perl[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Procedure Factorize(Number, List Factors())
  Protected I = 3, Max
  ClearList(Factors())
  While Number % 2 = 0
    AddElement(Factors())
    Factors() = 2
    Number / 2
  Wend
  Max = Number
  While I <= Max And Number > 1
    While Number % I = 0
      AddElement(Factors())
      Factors() = I
      Number / I
    Wend
    I + 2
  Wend
EndProcedure

If OpenConsole()
  NewList n()
  For a=1 To 20
    text$=RSet(Str(a),2)+"= "
    Factorize(a,n())
    If ListSize(n())
      ResetList(n())
      While NextElement(n())
        text$ + Str(n())
        If ListSize(n())-ListIndex(n())>1
          text$ + "*"
        EndIf
      Wend
    Else
      text$+Str(a) ; To handle the '1', which is not really a prime...
    EndIf
    PrintN(text$)
  Next a
EndIf
Output:
 1= 1
 2= 2
 3= 3
 4= 2*2
 5= 5
 6= 2*3
 7= 7
 8= 2*2*2
 9= 3*3
10= 2*5
11= 11
12= 2*2*3
13= 13
14= 2*7
15= 3*5
16= 2*2*2*2
17= 17
18= 2*3*3
19= 19
20= 2*2*5

Python[edit]

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[edit]

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[edit]

#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[edit]

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[edit]

(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

REXX[edit]

simple approach[edit]

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[edit]

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.

Ring[edit]

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

Ruby[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

(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[edit]

$ 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[edit]

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[edit]

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[edit]

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[edit]

Made minor modifications on the code I posted under Prime Decomposition.

Function CountFactors(n)
	If n = 1 Then
		CountFactors = 1
	Else
		arrP = Split(ListPrimes(n)," ")
		Set arrList = CreateObject("System.Collections.ArrayList")
		divnum = n
		Do Until divnum = 1
			'The -1 is to account for the null element of arrP
			For i = 0 To UBound(arrP)-1
				If divnum = 1 Then
					Exit For
				ElseIf divnum Mod arrP(i) = 0 Then
					divnum = divnum/arrP(i)
					arrList.Add arrP(i)
				End If
			Next
		Loop
		arrList.Sort
		For i = 0 To arrList.Count - 1
			If i = arrList.Count - 1 Then
				CountFactors = CountFactors & arrList(i)
			Else
				CountFactors = CountFactors & arrList(i) & " * "
			End If
		Next
	End If
End Function
 
Function IsPrime(n)
	If n = 2 Then
		IsPrime = True
	ElseIf n <= 1 Or n Mod 2 = 0 Then
		IsPrime = False
	Else
		IsPrime = True
		For i = 3 To Int(Sqr(n)) Step 2
			If n Mod i = 0 Then
				IsPrime = False
				Exit For
			End If
		Next
	End If
End Function
 
Function ListPrimes(n)
	ListPrimes = ""
	For i = 1 To n
		If IsPrime(i) Then
			ListPrimes = ListPrimes & i & " "
		End If
	Next
End Function

'Testing the fucntions.
WScript.StdOut.Write "2 = " & CountFactors(2)
WScript.StdOut.WriteLine
WScript.StdOut.Write "2144 = " & CountFactors(2144)
WScript.StdOut.WriteLine
Output:
2 = 2
2144 = 2 * 2 * 2 * 2 * 2 * 67

Visual Basic .NET[edit]

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)[edit]

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
...

XPL0[edit]

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

Wren[edit]

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

zkl[edit]

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[edit]

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