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{{task|Prime Numbers}}
;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.
<br> '''6''' is not prime; it would be shown as '''<math>2\times3</math>.'''
<br>'''2144''' is not prime; it would be shown as '''<math>2\times2\times2\times2\times2\times67</math>.'''
;Related tasks:
* [[prime decomposition]]
* [[factors of an integer]]
* [[Sieve of Eratosthenes]]
* [[primality by trial division]]
* [[factors of a Mersenne number]]
* [[trial factoring of a Mersenne number]]
* [[partition an integer X into N primes]]
<br><br>
=={{header|11l}}==
{{trans|C++}}<syntaxhighlight lang="11l">F get_prime_factors(=li)
I li == 1
R ‘1’
E
V res = ‘’
V f = 2
L
I li % f == 0
res ‘’= f
li /= f
I li == 1
L.break
res ‘’= ‘ x ’
E
f++
R res
L(x) 1..17
print(‘#4: #.’.format(x, get_prime_factors(x)))
print(‘2144: ’get_prime_factors(2144))</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|360 Assembly}}==
<syntaxhighlight lang="360asm">* 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</syntaxhighlight>
{{out}}
<pre style="height:20ex">
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
</pre>
=={{header|Action!}}==
<syntaxhighlight lang="action!">PROC PrintFactors(CARD a)
BYTE notFirst
CARD p
IF a=1 THEN
PrintC(a) RETURN
FI
p=2 notFirst=0
WHILE p<=a
DO
IF a MOD p=0 THEN
IF notFirst THEN
Put('x)
FI
notFirst=1
PrintC(p)
a==/p
ELSE
p==+1
FI
OD
RETURN
PROC Main()
CARD i
FOR i=1 TO 1000
DO
PrintC(i) Put('=)
PrintFactors(i)
PutE()
OD
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Count_in_factors.png Screenshot from Atari 8-bit computer]
<pre>
1=1
2=2
3=3
4=2x2
5=5
...
995=5x199
996=2x2x3x83
997=997
998=2x499
999=3x3x3x37
1000=2x2x2x5x5x5
</pre>
=={{header|Ada}}==
The solution uses the generic package Prime_Numbers from [[Prime decomposition#Ada]]
;count.adb:
<syntaxhighlight lang="ada">with Ada.Command_Line, Ada.Text_IO, Prime_Numbers;
procedure Count is
package Prime_Nums is new Prime_Numbers
(Number => Natural, Zero => 0, One => 1, Two => 2); use Prime_Nums;
procedure Put (List : Number_List) is
begin
Line 52 ⟶ 258:
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) & ": ");
Line 66 ⟶ 272:
exit when N > Max_N;
end loop;
end Count;</
{{out}}
<pre> 1: 1
2: 2
Line 84 ⟶ 290:
14: 2 x 7
15: 3 x 5</pre>
=={{header|ALGOL 68}}==
{{trans|Euphoria}}<syntaxhighlight lang="algol68">
OP +:= = (REF FLEX []INT a, INT b) VOID:
BEGIN
[UPB a + 1] INT c;
c[:UPB a] := a;
c[UPB a+1:] := b;
a := c
END;
PROC factorize = (INT nn) []INT:
BEGIN
IF nn = 1 THEN (1)
ELSE
INT k := 2, n := nn;
FLEX[0]INT result;
WHILE n > 1 DO
WHILE n MOD k = 0 DO
result +:= k;
n := n % k
OD;
k +:= 1
OD;
result
FI
END;
FLEX[0]INT factors;
FOR i TO 22 DO
factors := factorize (i);
print ((whole (i, 0), " = "));
FOR j TO UPB factors DO
(j /= 1 | print (" × "));
print ((whole (factors[j], 0)))
OD;
print ((new line))
OD
</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|ALGOL W}}==
<syntaxhighlight lang="algolw">
begin % show numbers and their prime factors %
% shows nand its prime factors %
procedure showFactors ( integer value n ) ;
if n <= 3 then write( i_w := 1, s_w := 0, n, ": ", n )
else begin
integer v, f; logical first;
first := true;
v := n;
write( i_w := 1, s_w := 0, n, ": " );
while not odd( v ) and v > 1 do begin
if not first then writeon( s_w := 0, " x " );
writeon( i_w := 1, s_w := 0, 2 );
v := v div 2;
first := false
end while_not_odd_v ;
f := 1;
while v > 1 do begin
f := f + 2;
while v rem f = 0 do begin
if not first then writeon( s_w := 0, " x " );
writeon( i_w := 1, s_w := 0, f );
v := v div f;
first := false
end while_v_rem_f_eq_0
end while_v_gt_0_and_f_le_v
end showFactors ;
% show the factors of various ranges - same as Wren %
for i := 1 until 9 do showFactors( i );
write( "... " );
for i := 2144 until 2154 do showFactors( i );
write( "... " );
for i := 9987 until 9999 do showFactors( i )
end.
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|ARM Assembly}}==
{{works with|as|Raspberry Pi}}
<syntaxhighlight lang="arm assembly">
/* ARM assembly Raspberry PI */
/* program countFactors.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes */
/************************************/
.include "../constantes.inc"
.equ NBFACT, 33
.equ MAXI, 1<<31
//.equ NOMBRE, 65537
//.equ NOMBRE, 99999999
.equ NOMBRE, 2144
//.equ NOMBRE, 529
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessNumber: .asciz "Number @ : "
szMessResultFact: .asciz "@ "
szCarriageReturn: .asciz "\n"
szErrorGen: .asciz "Program error !!!\n"
szMessPrime: .asciz "This number is prime.\n"
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
tbZoneDecom: .skip 8 * NBFACT // factor 4 bytes, number of each factor 4 bytes
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
ldr r7,iNombre @ number
mov r0,r7
ldr r1,iAdrsZoneConv
bl conversion10 @ call décimal conversion
ldr r0,iAdrszMessNumber
ldr r1,iAdrsZoneConv @ insert conversion in message
bl strInsertAtCharInc
bl affichageMess @ display message
mov r0,r7
ldr r1,iAdrtbZoneDecom
bl decompFact
cmp r0,#-1
beq 98f @ error ?
mov r1,r0
ldr r0,iAdrtbZoneDecom
bl displayDivisors
b 100f
98:
ldr r0,iAdrszErrorGen
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrszCarriageReturn: .int szCarriageReturn
iAdrszMessResultFact: .int szMessResultFact
iAdrszErrorGen: .int szErrorGen
iAdrsZoneConv: .int sZoneConv
iAdrtbZoneDecom: .int tbZoneDecom
iAdrszMessNumber: .int szMessNumber
iNombre: .int NOMBRE
/******************************************************************/
/* display divisors function */
/******************************************************************/
/* r0 contains address of divisors area */
/* r1 contains the number of area items */
displayDivisors:
push {r2-r8,lr} @ save registers
cmp r1,#0
beq 100f
mov r2,r1
mov r3,#0 @ indice
mov r4,r0
1:
add r5,r4,r3,lsl #3
ldr r7,[r5] @ load factor
ldr r6,[r5,#4] @ load number of factor
mov r8,#0 @ display factor counter
2:
mov r0,r7
ldr r1,iAdrsZoneConv
bl conversion10 @ call décimal conversion
ldr r0,iAdrszMessResultFact
ldr r1,iAdrsZoneConv @ insert conversion in message
bl strInsertAtCharInc
bl affichageMess @ display message
add r8,#1 @ increment counter
cmp r8,r6 @ same factors number ?
blt 2b
add r3,#1 @ other ithem
cmp r3,r2 @ items maxi ?
blt 1b
ldr r0,iAdrszCarriageReturn
bl affichageMess
b 100f
100:
pop {r2-r8,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* factor decomposition */
/******************************************************************/
/* r0 contains number */
/* r1 contains address of divisors area */
/* r0 return divisors items in table */
decompFact:
push {r1-r8,lr} @ save registers
mov r5,r1
mov r8,r0 @ save number
bl isPrime @ prime ?
cmp r0,#1
beq 98f @ yes is prime
mov r4,#0 @ raz indice
mov r1,#2 @ first divisor
mov r6,#0 @ previous divisor
mov r7,#0 @ number of same divisors
2:
mov r0,r8 @ dividende
bl division @ r1 divisor r2 quotient r3 remainder
cmp r3,#0
bne 5f @ if remainder <> zero -> no divisor
mov r8,r2 @ else quotient -> new dividende
cmp r1,r6 @ same divisor ?
beq 4f @ yes
cmp r6,#0 @ no but is the first divisor ?
beq 3f @ yes
str r6,[r5,r4,lsl #2] @ else store in the table
add r4,r4,#1 @ and increment counter
str r7,[r5,r4,lsl #2] @ store counter
add r4,r4,#1 @ next item
mov r7,#0 @ and raz counter
3:
mov r6,r1 @ new divisor
4:
add r7,r7,#1 @ increment counter
b 7f @ and loop
/* not divisor -> increment next divisor */
5:
cmp r1,#2 @ if divisor = 2 -> add 1
addeq r1,#1
addne r1,#2 @ else add 2
b 2b
/* divisor -> test if new dividende is prime */
7:
mov r3,r1 @ save divisor
cmp r8,#1 @ dividende = 1 ? -> end
beq 10f
mov r0,r8 @ new dividende is prime ?
mov r1,#0
bl isPrime @ the new dividende is prime ?
cmp r0,#1
bne 10f @ the new dividende is not prime
cmp r8,r6 @ else dividende is same divisor ?
beq 9f @ yes
cmp r6,#0 @ no but is the first divisor ?
beq 8f @ yes it is a first
str r6,[r5,r4,lsl #2] @ else store in table
add r4,r4,#1 @ and increment counter
str r7,[r5,r4,lsl #2] @ and store counter
add r4,r4,#1 @ next item
8:
mov r6,r8 @ new dividende -> divisor prec
mov r7,#0 @ and raz counter
9:
add r7,r7,#1 @ increment counter
b 11f
10:
mov r1,r3 @ current divisor = new divisor
cmp r1,r8 @ current divisor > new dividende ?
ble 2b @ no -> loop
/* end decomposition */
11:
str r6,[r5,r4,lsl #2] @ store last divisor
add r4,r4,#1
str r7,[r5,r4,lsl #2] @ and store last number of same divisors
add r4,r4,#1
lsr r0,r4,#1 @ return number of table items
mov r3,#0
str r3,[r5,r4,lsl #2] @ store zéro in last table item
add r4,r4,#1
str r3,[r5,r4,lsl #2] @ and zero in counter same divisor
b 100f
98:
ldr r0,iAdrszMessPrime
bl affichageMess
mov r0,#1 @ return code
b 100f
99:
ldr r0,iAdrszErrorGen
bl affichageMess
mov r0,#-1 @ error code
b 100f
100:
pop {r1-r8,lr} @ restaur registers
bx lr
iAdrszMessPrime: .int szMessPrime
/***************************************************/
/* check if a number is prime */
/***************************************************/
/* r0 contains the number */
/* r0 return 1 if prime 0 else */
@2147483647
@4294967297
@131071
isPrime:
push {r1-r6,lr} @ save registers
cmp r0,#0
beq 90f
cmp r0,#17
bhi 1f
cmp r0,#3
bls 80f @ for 1,2,3 return prime
cmp r0,#5
beq 80f @ for 5 return prime
cmp r0,#7
beq 80f @ for 7 return prime
cmp r0,#11
beq 80f @ for 11 return prime
cmp r0,#13
beq 80f @ for 13 return prime
cmp r0,#17
beq 80f @ for 17 return prime
1:
tst r0,#1 @ even ?
beq 90f @ yes -> not prime
mov r2,r0 @ save number
sub r1,r0,#1 @ exposant n - 1
mov r0,#3 @ base
bl moduloPuR32 @ compute base power n - 1 modulo n
cmp r0,#1
bne 90f @ if <> 1 -> not prime
mov r0,#5
bl moduloPuR32
cmp r0,#1
bne 90f
mov r0,#7
bl moduloPuR32
cmp r0,#1
bne 90f
mov r0,#11
bl moduloPuR32
cmp r0,#1
bne 90f
mov r0,#13
bl moduloPuR32
cmp r0,#1
bne 90f
mov r0,#17
bl moduloPuR32
cmp r0,#1
bne 90f
80:
mov r0,#1 @ is prime
b 100f
90:
mov r0,#0 @ no prime
100: @ fin standard de la fonction
pop {r1-r6,lr} @ restaur des registres
bx lr @ retour de la fonction en utilisant lr
/********************************************************/
/* Calcul modulo de b puissance e modulo m */
/* Exemple 4 puissance 13 modulo 497 = 445 */
/* */
/********************************************************/
/* r0 nombre */
/* r1 exposant */
/* r2 modulo */
/* r0 return result */
moduloPuR32:
push {r1-r7,lr} @ save registers
cmp r0,#0 @ verif <> zero
beq 100f
cmp r2,#0 @ verif <> zero
beq 100f @
1:
mov r4,r2 @ save modulo
mov r5,r1 @ save exposant
mov r6,r0 @ save base
mov r3,#1 @ start result
mov r1,#0 @ division de r0,r1 par r2
bl division32R
mov r6,r2 @ base <- remainder
2:
tst r5,#1 @ exposant even or odd
beq 3f
umull r0,r1,r6,r3
mov r2,r4
bl division32R
mov r3,r2 @ result <- remainder
3:
umull r0,r1,r6,r6
mov r2,r4
bl division32R
mov r6,r2 @ base <- remainder
lsr r5,#1 @ left shift 1 bit
cmp r5,#0 @ end ?
bne 2b
mov r0,r3
100: @ fin standard de la fonction
pop {r1-r7,lr} @ restaur des registres
bx lr @ retour de la fonction en utilisant lr
/***************************************************/
/* division number 64 bits in 2 registers by number 32 bits */
/***************************************************/
/* r0 contains lower part dividende */
/* r1 contains upper part dividende */
/* r2 contains divisor */
/* r0 return lower part quotient */
/* r1 return upper part quotient */
/* r2 return remainder */
division32R:
push {r3-r9,lr} @ save registers
mov r6,#0 @ init upper upper part remainder !!
mov r7,r1 @ init upper part remainder with upper part dividende
mov r8,r0 @ init lower part remainder with lower part dividende
mov r9,#0 @ upper part quotient
mov r4,#0 @ lower part quotient
mov r5,#32 @ bits number
1: @ begin loop
lsl r6,#1 @ shift upper upper part remainder
lsls r7,#1 @ shift upper part remainder
orrcs r6,#1
lsls r8,#1 @ shift lower part remainder
orrcs r7,#1
lsls r4,#1 @ shift lower part quotient
lsl r9,#1 @ shift upper part quotient
orrcs r9,#1
@ divisor sustract upper part remainder
subs r7,r2
sbcs r6,#0 @ and substract carry
bmi 2f @ négative ?
@ positive or equal
orr r4,#1 @ 1 -> right bit quotient
b 3f
2: @ negative
orr r4,#0 @ 0 -> right bit quotient
adds r7,r2 @ and restaur remainder
adc r6,#0
3:
subs r5,#1 @ decrement bit size
bgt 1b @ end ?
mov r0,r4 @ lower part quotient
mov r1,r9 @ upper part quotient
mov r2,r7 @ remainder
100: @ function end
pop {r3-r9,lr} @ restaur registers
bx lr
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"
</syntaxhighlight>
<pre>
Number 2144 : 2 2 2 2 2 67
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">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]
]</syntaxhighlight>
{{out}}
<pre> 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</pre>
=={{header|AutoHotkey}}==
{{trans|D}}
<syntaxhighlight lang="autohotkey">factorize(n){
if n = 1
return 1
if n < 1
return false
result := 0, m := n, k := 2
While n >= k{
while !Mod(m, k){
result .= " * " . k, m /= k
}
k++
}
return SubStr(result, 5)
}
Loop 22
out .= A_Index ": " factorize(A_index) "`n"
MsgBox % out</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f COUNT_IN_FACTORS.AWK
BEGIN {
fmt = "%d=%s\n"
for (i=1; i<=16; i++) {
printf(fmt,i,factors(i))
}
i = 2144; printf(fmt,i,factors(i))
i = 6358; printf(fmt,i,factors(i))
exit(0)
}
function factors(n, f,p) {
if (n == 1) {
return(1)
}
p = 2
while (p <= n) {
if (n % p == 0) {
f = sprintf("%s%s*",f,p)
n /= p
}
else {
p++
}
}
return(substr(f,1,length(f)-1))
}
</syntaxhighlight>
<p>output:</p>
<pre>
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
</pre>
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
<syntaxhighlight lang="applesoftbasic"> 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$,O)
320 RETURN </syntaxhighlight>
==={{header|BASIC256}}===
{{trans|Run BASIC}}
<syntaxhighlight lang="freebasic">for i = 1 to 20
print i; " = "; factorial$(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</syntaxhighlight>
==={{header|Chipmunk Basic}}===
{{works with|Chipmunk Basic|3.6.4}}
{{trans|Run BASIC}}
<syntaxhighlight lang="qbasic">100 cls
110 for i = 1 to 20
120 rem for i = 1000 to 1016
130 print i;"= ";factorial$(i)
140 next i
150 end
160 function factorial$(num)
170 factor$ = "" : x$ = ""
180 if num = 1 then print "1"
190 fct = 2
200 while fct <= num
210 if (num mod fct) = 0 then
220 factor$ = factor$+x$+str$(fct)
230 x$ = " x "
240 num = num/fct
250 else
260 fct = fct+1
270 endif
280 wend
290 print factor$
300 end function</syntaxhighlight>
==={{header|True BASIC}}===
{{trans|Run BASIC}}
<syntaxhighlight lang="qbasic">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$(i)
NEXT i
END</syntaxhighlight>
==={{header|Yabasic}}===
{{trans|Run BASIC}}
<syntaxhighlight lang="freebasic">for i = 1 to 20
print i, " = ", factorial$(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</syntaxhighlight>
=={{header|BBC BASIC}}==
<syntaxhighlight lang="bbcbasic"> 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)
</syntaxhighlight>
Output:
<pre> 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</pre>
=={{header|Befunge}}==
Lists the first 100 entries in the sequence. If you wish to extend that, the upper limit is implementation dependent, but may be as low as 130 for an interpreter with signed 8 bit data cells (131 is the first prime outside that range).
<syntaxhighlight lang="befunge">1>>>>:.48*"=",,::1-#v_.v
$<<<^_@#-"e":+1,+55$2<<<
v4_^#-1:/.:g00_00g1+>>0v
>8*"x",,:00g%!^!%g00:p0<</syntaxhighlight>
{{out}}
<pre>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
.
.
.</pre>
=={{header|C}}==
Code includes a dynamically extending prime number list. The program doesn't stop until you kill it, or it runs out of memory, or it overflows.
<syntaxhighlight lang="c">#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;
}</syntaxhighlight>
{{out}}
<pre>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
.
.
.</pre>
=={{header|C sharp|C#}}==
<syntaxhighlight lang="csharp">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;
}
}
}</syntaxhighlight>
=={{header|C++}}==
<syntaxhighlight lang="cpp">#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" );
}</syntaxhighlight>
{{out}}
<pre>
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
.
.
.
</pre>
=={{header|Clojure}}==
<syntaxhighlight lang="lisp">(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))))
</syntaxhighlight>
{{Output}}
<pre>
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
</pre>
=={{header|CoffeeScript}}==
<syntaxhighlight lang="coffeescript">count_primes = (max) ->
# Count through the natural numbers and give their prime
# factorization. This algorithm uses no division.
# Instead, each prime number starts a rolling odometer
# to help subsequent factorizations. The algorithm works similar
# to the Sieve of Eratosthenes, as we note when each prime number's
# odometer rolls a digit. (As it turns out, as long as your computer
# is not horribly slow at division, you're better off just doing simple
# prime factorizations on each new n vs. using this algorithm.)
console.log "1 = 1"
primes = []
n = 2
while n <= max
factors = []
for prime_odometer in primes
# digits are an array w/least significant digit in
# position 0; for example, [3, [0]] will roll as
# follows:
# [0] -> [1] -> [2] -> [0, 1]
[base, digits] = prime_odometer
i = 0
while true
digits[i] += 1
break if digits[i] < base
digits[i] = 0
factors.push base
i += 1
if i >= digits.length
digits.push 0
if factors.length == 0
primes.push [n, [0, 1]]
factors.push n
console.log "#{n} = #{factors.join('*')}"
n += 1
primes.length
num_primes = count_primes 10000
console.log num_primes</syntaxhighlight>
=={{header|Common Lisp}}==
Auto extending prime list:
<syntaxhighlight lang="lisp">(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))))</syntaxhighlight>
{{out}}
<pre>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
...</pre>
Without saving the primes, and not all that much slower (probably because above code was not well-written):
<syntaxhighlight lang="lisp">(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))))</syntaxhighlight>
=={{header|D}}==
<syntaxhighlight lang="d">int[] factorize(in int n) pure nothrow
in {
assert(n > 0);
} body {
if (n == 1) return [1];
int[] result;
int m = n, k = 2;
while (n >= k) {
while (m % k == 0) {
result ~= k;
m /= k;
}
k++;
}
return result;
}
void main() {
import std.stdio;
foreach (i; 1 .. 22)
writefln("%d: %(%d × %)", i, i.factorize());
}</syntaxhighlight>
{{out}}
<pre>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</pre>
===Alternative Version===
{{libheader|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 ).
<
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)
foreach (p; Primes(limit)) {
if (n == 1) break
if (0UL == (n % p
while((n > 1) && (0UL == (n % p ))) {
res ~= p
n /=
}
}
if (n > 1)
res ~= [n]
return res
}
string productStr(T)(in T[] nums) {
return
}
void main() {
foreach (i; 1 .. 21)
writefln("%2d = %s", i, productStr(factorize(i)))
}</
=={{header|
Assumes file primes.txt is a list of prime numbers;
<syntaxhighlight lang="dcl">$ 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</syntaxhighlight>
{{out}}
<pre>$ @count_in_factors
1 = 1
2 = 2
3 = 3
4 = 2*2
5 = 5
6 = 2*3
...
2144 = 2*2*2*2*2*67</pre>
=={{header|Delphi}}==
See [https://rosettacode.org/wiki/Count_in_factors#Pascal Pascal].
=={{header|DWScript}}==
<syntaxhighlight lang="delphi">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));</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
proc decompose num . primes[] .
primes[] = [ ]
t = 2
while t * t <= num
if num mod t = 0
primes[] &= t
num = num / t
else
t += 1
.
.
primes[] &= num
.
for i = 1 to 30
write i & ": "
decompose i primes[]
for j = 1 to len primes[]
if j > 1
write " x "
.
write primes[j]
.
print ""
primes[] = [ ]
.
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|EchoLisp}}==
<syntaxhighlight lang="scheme">
(define (task (nfrom 2) (range 20))
(for ((i (in-range nfrom (+ nfrom range))))
(writeln i "=" (string-join (prime-factors i) " x "))))
</syntaxhighlight>
{{out}}
<pre>
(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
</pre>
=={{header|Eiffel}}==
<syntaxhighlight lang="eiffel">
class
COUNT_IN_FACTORS
feature
display_factor (p: INTEGER)
-- Factors of all integers up to 'p'.
require
p_positive: p > 0
local
factors: ARRAY [INTEGER]
do
across
1 |..| p as c
loop
io.new_line
io.put_string (c.item.out + "%T")
factors := factor (c.item)
across
factors as f
loop
io.put_integer (f.item)
if f.is_last = False then
io.put_string (" x ")
end
end
end
end
factor (p: INTEGER): ARRAY [INTEGER]
-- Prime decomposition of 'p'.
require
p_positive: p > 0
local
div, i, next, rest: INTEGER
do
create Result.make_empty
if p = 1 then
Result.force (1, 1)
end
div := 2
next := 3
rest := p
from
i := 1
until
rest = 1
loop
from
until
rest \\ div /= 0
loop
Result.force (div, i)
rest := (rest / div).floor
i := i + 1
end
div := next
next := next + 2
end
ensure
is_divisor: across Result as r all p \\ r.item = 0 end
end
end
</syntaxhighlight>
Test Output:
<pre>
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
</pre>
=={{header|Elixir}}==
<syntaxhighlight lang="elixir">defmodule RC do
def factor(n), do: factor(n, 2, [])
def factor(n, i, fact) when n < i*i, do: Enum.reverse([n|fact])
def factor(n, i, fact) do
if rem(n,i)==0, do: factor(div(n,i), i, [i|fact]),
else: factor(n, i+1, fact)
end
end
Enum.each(1..20, fn n ->
IO.puts "#{n}: #{Enum.join(RC.factor(n)," x ")}" end)</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Euphoria}}==
<syntaxhighlight lang="euphoria">function factorize(integer n)
sequence result
integer k
if n = 1 then
return {1}
else
k = 2
result = {}
while n > 1 do
while remainder(n, k) = 0 do
result &= k
n /= k
end while
k += 1
end while
return result
end if
end function
sequence factors
for i = 1 to 22 do
printf(1, "%d: ", i)
factors = factorize(i)
for j = 1 to length(factors)-1 do
printf(1, "%d * ", factors[j])
end for
printf(1, "%d\n", factors[$])
end for</syntaxhighlight>
{{out}}
<pre>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
</pre>
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">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)))</syntaxhighlight>
{{out}}
<pre>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
:
</pre>
=={{header|Factor}}==
<syntaxhighlight lang="factor">USING: io kernel math.primes.factors math.ranges prettyprint
sequences ;
: .factors ( n -- )
dup pprint ": " write factors
[ " × " write ] [ pprint ] interleave nl ;
"1: 1" print 2 20 [a,b] [ .factors ] each</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Forth}}==
<syntaxhighlight lang="forth">: .factors ( n -- )
2
begin 2dup dup * >=
while 2dup /mod swap
if drop 1+ 1 or \ next odd number
else -rot nip dup . ." x "
then
repeat
drop . ;
: main ( n -- )
." 1 : 1" cr
1+ 2 ?do i . ." : " i .factors cr loop ;
15 main bye</syntaxhighlight>
=={{header|Fortran}}==
Please find the example output along with the build instructions in the comments at the start of the FORTRAN 2008 source. Compiler: gfortran from the GNU compiler collection. Command interpreter: bash. The code writes j assertions which don't prove primality of the factors but does prove they are the factors.
This algorithm creates a sieve of Eratosthenes, storing the largest prime factor to mark composites. It then finds prime factors by repeatedly looking up the value in the sieve, then dividing by the factor found until the value is itself prime. Using the sieve table to store factors rather than as a plain bitmap was to me a novel idea.
<syntaxhighlight lang="fortran">
!-*- 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
</syntaxhighlight>
=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">' FB 1.05.0 Win64
Sub getPrimeFactors(factors() As UInteger, n As UInteger)
If n < 2 Then Return
Dim factor As UInteger = 2
Do
If n Mod factor = 0 Then
Redim Preserve factors(0 To UBound(factors) + 1)
factors(UBound(factors)) = factor
n \= factor
If n = 1 Then Return
Else
factor += 1
End If
Loop
End Sub
Dim factors() As UInteger
For i As UInteger = 1 To 20
Print Using "##"; i;
Print " = ";
If i > 1 Then
Erase factors
getPrimeFactors factors(), i
For j As Integer = LBound(factors) To UBound(factors)
Print factors(j);
If j < UBound(factors) Then Print " x ";
Next j
Print
Else
Print i
End If
Next i
Print
Print "Press any key to quit"
Sleep</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Frink}}==
Frink's factoring routines work on arbitrarily-large integers.
<syntaxhighlight lang="frink">i = 1
while true
{
println[join[" x ", factorFlat[i]]]
i = i + 1
}</syntaxhighlight>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
local fn Factorial( num as long ) as CFStringRef
CFStringRef x, f, result
long fct
f = @"" : x = @""
if num = 1 then result = @" 1" : exit fn
fct = 2
while ( fct <= num )
if ( num mod fct == 0 )
f = fn StringWithFormat( @"%@%@%@", f, x, str( fct ) )
x = @" x"
num = num / fct
else
fct++
end if
wend
result = f
end fn = result
long i
for i = 1 to 20
printf @"%2ld =%@", i, fn Factorial(i)
next
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
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
</pre>
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Count_in_factors}}
'''Solution'''
The '''Factor''' expression reduces to a list of the primer factors of a given number.
We cannot create the multiplication directly, because it would be reduced immediately to its value. We can make use of the reflection capabilities:
[[File:Fōrmulæ - Count in factors 01.png]]
[[File:Fōrmulæ - Count in factors 02.png]]
[[File:Fōrmulæ - Count in factors 03.png]]
[[File:Fōrmulæ - Count in factors 04.png]]
[[File:Fōrmulæ - Count in factors 05.png]]
=={{header|Go}}==
<syntaxhighlight lang="go">package main
import "fmt"
func main() {
fmt.Println("1: 1")
for i := 2; ; i++ {
fmt.Printf("%d: ", i)
var x string
for n, f := i, 2; n != 1; f++ {
for m := n % f; m == 0; m = n % f {
fmt.Print(x, f)
x = "×"
n /= f
}
}
fmt.Println()
}
}</syntaxhighlight>
{{out}}
<pre>
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
...
</pre>
=={{header|Groovy}}==
<syntaxhighlight lang="groovy">def factors(number) {
if (number == 1) {
return [1]
}
def factors = []
BigInteger value = number
BigInteger possibleFactor = 2
while (possibleFactor <= value) {
if (value % possibleFactor == 0) {
factors << possibleFactor
value /= possibleFactor
} else {
possibleFactor++
}
}
factors
}
Number.metaClass.factors = { factors(delegate) }
((1..10) + (6351..6359)).each { number ->
println "$number = ${number.factors().join(' x ')}"
}</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|Haskell}}==
Using <code>factorize</code> function from the [[Prime_decomposition#Haskell|prime decomposition]] task,
<syntaxhighlight lang="haskell">import Data.List (intercalate)
showFactors n = show n ++ " = " ++ (intercalate " * " . map show . factorize) n
-- Pointfree form
showFactors = ((++) . show) <*> ((" = " ++) . intercalate " * " . map show . factorize)</syntaxhighlight>
isPrime n = n > 1 && noDivsBy primeNums n
{{out}}
<small><syntaxhighlight lang="haskell">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
. . .</syntaxhighlight></small>
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.
=={{header|Icon}} and {{header|Unicon}}==
<syntaxhighlight lang="icon">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</syntaxhighlight>
{{libheader|Icon Programming Library}}
[http://www.cs.arizona.edu/icon/library/src/procs/factors.icn factors.icn provides factors]
{{out}}
<pre>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 ]
...</pre>
=={{header|IS-BASIC}}==
<syntaxhighlight lang="is-basic">100 PROGRAM "Factors.bas"
110 FOR I=1 TO 30
120 PRINT I;"= ";FACTORS$(I)
130 NEXT
140 DEF FACTORS$(N)
150 LET F$=""
160 IF N=1 THEN
170 LET FACTORS$="1"
180 ELSE
190 LET P=2
200 DO WHILE P<=N
210 IF MOD(N,P)=0 THEN
220 LET F$=F$&STR$(P)&"*"
230 LET N=INT(N/P)
240 ELSE
250 LET P=P+1
260 END IF
270 LOOP
280 LET FACTORS$=F$(1:LEN(F$)-1)
290 END IF
300 END DEF</syntaxhighlight>
{{out}}
<pre> 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</pre>
=={{header|J}}==
'''Solution''':Use J's factoring primitive, <syntaxhighlight lang="j">q:</syntaxhighlight>
'''Example''' (including formatting):<syntaxhighlight lang="j"> ('1 : 1',":&> ,"1 ': ',"1 ":@q:) 2+i.10
1 : 1
2 : 2
Line 134 ⟶ 2,551:
9 : 3 3
10: 2 5
11: 11</
=={{header|
{{trans|Visual Basic .NET}}
<syntaxhighlight lang="java">public class CountingInFactors{
public static void main(String[] args){
for(int i = 1; i<= 10; i++){
System.out.println(i + " = "+ countInFactors(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;
}
}</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|JavaScript}}==
<syntaxhighlight lang="javascript">for(i = 1; i <= 10; i++)
console.log(i + " : " + factor(i).join(" x "));
function factor(n) {
var factors = [];
if (n
for(p =
if((n % p) == 0) {
factors[factors.length] = p;
n /= p;
}
else p++;
}
return factors;
}</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
The following uses `factors/0`, a suitable implementation of which may be found at
[[Prime_decomposition#jq]].
gojq supports unlimited-precision integer arithmetic, but the C implementation of jq
currently uses IEEE 754 64-bit numbers, so using the latter, the following program will only be
reliable for integers up to and including 9,007,199,254,740,992 (2^53). However, "factors"
could be easily modified to work with a "BigInt" library for jq, such as [https://gist.github.com/pkoppstein/d06a123f30c033195841 BigInt.jq].
<syntaxhighlight lang="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"))");
</syntaxhighlight>
'''Examples'''
<syntaxhighlight lang="jq">
10 | count_in_factors,
"",
count_in_factors(2144; 2145),
"",
(2|power(100) | count_in_factors(.; .+ 2))</syntaxhighlight>
{{out}}
The output shown here is based on a run of gojq.
<pre>
1: 1
2: 2
3: 3
4: 2x2
5: 5
6: 2x3
7: 7
8: 2x2x2
9: 3x3
2144: 2x2x2x2x2x67
1267650600228229401496703205376: 2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2
1267650600228229401496703205377: 17x401x61681x340801x2787601x3173389601
</pre>
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Primes, Printf
function strfactor(n::Integer)
n > -2 || return "-1 × " * strfactor(-n)
isprime(n) || n < 2 && return dec(n)
f = factor(Vector{typeof(n)}, n)
return join(f, " × ")
end
lo, hi = -4, 40
println("Factor print $lo to $hi:")
for n in lo:hi
@printf("%5d = %s\n", n, strfactor(n))
end</syntaxhighlight>
{{out}}
<pre>Factor print -4 to 40:
-4 = -1 × 2 × 2
-3 = -1 × 3
-2 = -1 × 2
-1 = -1
0 = 0
1 = 1
2 = 2
3 = 3
4 = 2 × 2
5 = 5
6 = 2 × 3
7 = 7
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
11 = 11
12 = 2 × 2 × 3
13 = 13
14 = 2 × 7
15 = 3 × 5
16 = 2 × 2 × 2 × 2
17 = 17
18 = 2 × 3 × 3
19 = 19
20 = 2 × 2 × 5
21 = 3 × 7
22 = 2 × 11
23 = 23
24 = 2 × 2 × 2 × 3
25 = 5 × 5
26 = 2 × 13
27 = 3 × 3 × 3
28 = 2 × 2 × 7
29 = 29
30 = 2 × 3 × 5
31 = 31
32 = 2 × 2 × 2 × 2 × 2
33 = 3 × 11
34 = 2 × 17
35 = 5 × 7
36 = 2 × 2 × 3 × 3
37 = 37
38 = 2 × 19
39 = 3 × 13
40 = 2 × 2 × 2 × 5</pre>
=={{header|Kotlin}}==
<syntaxhighlight lang="scala">// version 1.1.2
fun isPrime(n: Int) : Boolean {
if (n < 2) return false
if (n % 2 == 0) return n == 2
if (n % 3 == 0) return n == 3
var d = 5
while (d * d <= n) {
if (n % d == 0) return false
d += 2
if (n % d == 0) return false
d += 4
}
return true
}
fun getPrimeFactors(n: Int): List<Int> {
val factors = mutableListOf<Int>()
if (n < 1) return factors
if (n == 1 || isPrime(n)) {
factors.add(n)
return factors
}
var factor = 2
var nn = n
while (true) {
if (nn % factor == 0) {
factors.add(factor)
nn /= factor
if (nn == 1) return factors
if (isPrime(nn)) factor = nn
}
else if (factor >= 3) factor += 2
else factor = 3
}
}
fun main(args: Array<String>) {
val list = (MutableList(22) { it + 1 } + 2144) + 6358
for (i in list)
println("${"%4d".format(i)} = ${getPrimeFactors(i).joinToString(" * ")}")
}</syntaxhighlight>
{{out}}
<pre>
1 = 1
2 = 2
3 = 3
4 = 2 * 2
5 = 5
6 = 2 * 3
7 = 7
8 = 2 * 2 * 2
9 = 3 * 3
10 = 2 * 5
11 = 11
12 = 2 * 2 * 3
13 = 13
14 = 2 * 7
15 = 3 * 5
16 = 2 * 2 * 2 * 2
17 = 17
18 = 2 * 3 * 3
19 = 19
20 = 2 * 2 * 5
21 = 3 * 7
22 = 2 * 11
2144 = 2 * 2 * 2 * 2 * 2 * 67
6358 = 2 * 11 * 17 * 17
</pre>
=={{header|Liberty BASIC}}==
<syntaxhighlight lang="lb">
'see Run BASIC solution
for i = 1000 to 1016
print i;" = "; factorial$(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 </syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Lua}}==
<syntaxhighlight lang="lua">function factorize( n )
if n == 1 then return {1} end
local k = 2
res = {}
while n > 1 do
while n % k == 0 do
res[#res+1] = k
n = n / k
end
k = k + 1
end
return res
end
for i = 1, 22 do
io.write( i, ": " )
fac = factorize( i )
io.write( fac[1] )
for j = 2, #fac do
io.write( " * ", fac[j] )
end
print ""
end</syntaxhighlight>
=={{header|M2000 Interpreter}}==
Decompose function now return array (in number decomposition task return an inventory list).
<syntaxhighlight lang="m2000 interpreter">
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
</syntaxhighlight>
=={{header|M4}}==
<syntaxhighlight lang="m4">define(`for',
`ifelse($#,0,``$0'',
`ifelse(eval($2<=$3),1,
`pushdef(`$1',$2)$5`'popdef(`$1')$0(`$1',eval($2+$4),$3,$4,`$5')')')')dnl
define(`by',
`ifelse($1,$2,
$1,
`ifelse(eval($1%$2==0),1,
`$2 x by(eval($1/$2),$2)',
`by($1,eval($2+1))') ') ')dnl
define(`wby',
`$1 = ifelse($1,1,
$1,
`by($1,2)') ')dnl
for(`y',1,25,1, `wby(y)
')</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Maple}}==
<syntaxhighlight lang="maple">factorNum := proc(n)
local i, j, firstNum;
if n = 1 then
printf("%a", 1);
end if;
firstNum := true:
for i in ifactors(n)[2] do
for j to i[2] do
if firstNum then
printf ("%a", i[1]);
firstNum := false:
else
printf(" x %a", i[1]);
end if;
end do;
end do;
printf("\n");
return NULL;
end proc:
for i from 1 to 10 do
printf("%2a: ", i);
factorNum(i);
end do;</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">n = 2;
While[n < 100,
Print[Row[Riffle[Flatten[Map[Apply[ConstantArray, #] &, FactorInteger[n]]],"*"]]];
n++]</syntaxhighlight>
=={{header|NetRexx}}==
{{trans|Java}}
<syntaxhighlight lang="netrexx">/* NetRexx */
options replace format comments java crossref symbols nobinary
runSample(arg)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method factor(val) public static
rv = 1
if val > 1 then do
rv = ''
loop n_ = val until n_ = 1
parse checkFactor(2, n_, rv) n_ rv
if n_ = 1 then leave n_
parse checkFactor(3, n_, rv) n_ rv
if n_ = 1 then leave n_
loop m_ = 5 to n_ by 2 until n_ = 1
if m_ // 3 = 0 then iterate m_
parse checkFactor(m_, n_, rv) n_ rv
end m_
end n_
end
return rv
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method checkFactor(mult = long, n_ = long, fac) private static binary
msym = 'x'
loop while n_ // mult = 0
fac = fac msym mult
n_ = n_ % mult
end
fac = (fac.strip).strip('l', msym).space
return n_ fac
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
-- input is a list of pairs of numbers - no checking is done
if arg = '' then arg = '1 11 89 101 1000 1020 10000 10010'
loop while arg \= ''
parse arg lv rv arg
say
say '-'.copies(60)
say lv.right(8) 'to' rv
say '-'.copies(60)
loop fv = lv to rv
fac = factor(fv)
pv = ''
if fac.words = 1 & fac \= 1 then pv = '<prime>'
say fv.right(8) '=' fac pv
end fv
end
return
</syntaxhighlight>
{{out}}
<pre style="height: 30em;overflow: scroll; font-size: smaller;">
------------------------------------------------------------
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
</pre>
=={{header|Nim}}==
{{trans|C}}
<syntaxhighlight lang="nim">var primes = newSeq[int]()
proc getPrime(idx: int): int =
if idx >= primes.len:
if primes.len == 0:
primes.add 2
primes.add 3
var last = primes[primes.high]
while idx >= primes.len:
last += 2
for i, p in primes:
if p * p > last:
primes.add last
break
if last mod p == 0:
break
return primes[idx]
for x in 1 ..< int32.high.int:
stdout.write x, " = "
var n = x
var first = true
for i in 0 ..< int32.high:
let p = getPrime(i)
while n mod p == 0:
n = n div p
if not first: stdout.write " x "
first = false
stdout.write p
if n <= p * p:
break
if first > 0: echo n
elif n > 1: echo " x ", n
else: echo ""</syntaxhighlight>
<pre>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
...</pre>
=={{header|Objeck}}==
<syntaxhighlight lang="objeck">
class CountingInFactors {
function : Main(args : String[]) ~ Nil {
for(i := 1; i <= 10; i += 1;){
count := CountInFactors(i);
("{$i} = {$count}")->PrintLine();
};
for(i := 9991; i <= 10000; i += 1;){
count := CountInFactors(i);
("{$i} = {$count}")->PrintLine();
};
}
function : CountInFactors(n : Int) ~ String {
if(n = 1) {
return "1";
};
sb := "";
n := CheckFactor(2, n, sb);
if(n = 1) {
return sb;
};
n := CheckFactor(3, n, sb);
if(n = 1) {
return sb;
};
for(i := 5; i <= n; i += 2;) {
if(i % 3 <> 0) {
n := CheckFactor(i, n, sb);
if(n = 1) {
break;
};
};
};
return sb;
}
function : CheckFactor(mult : Int, n : Int, sb : String) ~ Int {
while(n % mult = 0 ) {
if(sb->Size() > 0) {
sb->Append(" x ");
};
sb->Append(mult);
n /= mult;
};
return n;
}
}
</syntaxhighlight>
Output:
<pre>
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
9991 = 97 x 103
9992 = 2 x 2 x 2 x 1249
9993 = 3 x 3331
9994 = 2 x 19 x 263
9995 = 5 x 1999
9996 = 2 x 2 x 3 x 7 x 7 x 17
9997 = 13 x 769
9998 = 2 x 4999
9999 = 3 x 3 x 11 x 101
10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
</pre>
=={{header|OCaml}}==
<syntaxhighlight lang="ocaml">open Big_int
let prime_decomposition x =
let rec inner c p =
if lt_big_int p (square_big_int c) then
[p]
else if eq_big_int (mod_big_int p c) zero_big_int then
c :: inner c (div_big_int p c)
else
inner (succ_big_int c) p
in
inner (succ_big_int (succ_big_int zero_big_int)) x
let () =
let rec aux v =
let ps = prime_decomposition v in
print_string (string_of_big_int v);
print_string " = ";
print_endline (String.concat " x " (List.map string_of_big_int ps));
aux (succ_big_int v)
in
aux unit_big_int</syntaxhighlight>
{{out|Execution}}
<pre>$ 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</pre>
=={{header|Octave}}==
Octave's factor function returns an array:
<syntaxhighlight lang="octave">for (n = 1:20)
printf ("%i: ", n)
printf ("%i ", factor (n))
printf ("\n")
endfor</syntaxhighlight>
{{out}}
<pre>1: 1
2: 2
3: 3
4: 2
5: 5
6: 2
7: 7
8: 2
9: 3
10: 2
11: 11
12: 2
13: 13
14: 2
15: 3
16: 2
17: 17
18: 2
19: 19
20: 2
=={{header|PARI/GP}}==
<syntaxhighlight lang="parigp">
fnice(n)={
my(f,s="",s1);
if (n < 2, return(n));
f = factor(n);
s = Str(s, f[1,1]);
if (f[1, 2] != 1, s=Str(s, "^", f[1,2]));
for(i=2,#f[,1], s1 = Str(" * ", f[i, 1]); if (f[i, 2] != 1, s1 = Str(s1, "^", f[i, 2])); s = Str(s, s1));
s
};
n=0;while(n++<21, printf("%2s: %s\n",n,fnice(n)))
</syntaxhighlight>
{{out}}
<pre>
1: 1
2: 2
3: 3
4: 2^2
5: 5
6: 2 * 3
7: 7
8: 2^3
9: 3^2
10: 2 * 5
11: 11
12: 2^2 * 3
13: 13
14: 2 * 7
15: 3 * 5
16: 2^4
17: 17
18: 2 * 3^2
19: 19
20: 2^2 * 5
</pre>
=={{header|Pascal}}==
{{works with|Free_Pascal}}
<syntaxhighlight lang="pascal">program CountInFactors(output);
{$IFDEF FPC}
{$MODE DELPHI}
{$ENDIF}
type
TdynArray = array of integer;
function factorize(number: integer): TdynArray;
var
k: integer;
begin
if number = 1 then
begin
setlength(Result, 1);
Result[0] := 1
end
else
begin
k := 2;
while number > 1 do
begin
while number mod k = 0 do
begin
setlength(Result, length(Result) + 1);
Result[high(Result)] := k;
number := number div k;
end;
inc(k);
end;
end
end;
var
i, j: integer;
fac: TdynArray;
begin
for i := 1 to 22 do
begin
write(i, ': ' );
fac := factorize(i);
write(fac[0]);
for j := 1 to high(fac) do
write(' * ', fac[j]);
writeln;
end;
end.</syntaxhighlight>
{{out}}
<pre>
1: 1
2: 2
3: 3
4: 2 * 2
5: 5
6: 2 * 3
7: 7
8: 2 * 2 * 2
9: 3 * 3
10: 2 * 5
11: 11
12: 2 * 2 * 3
13: 13
14: 2 * 7
15: 3 * 5
16: 2 * 2 * 2 * 2
17: 17
18: 2 * 3 * 3
19: 19
20: 2 * 2 * 5
21: 3 * 7
22: 2 * 11
</pre>
=={{header|Perl}}==
Typically one would use a module for this. Note that these modules all return an empty list for '1'. This should be efficient to 50+ digits:{{libheader|ntheory}}
<syntaxhighlight lang="perl">use ntheory qw/factor/;
print "$_ = ", join(" x ", factor($_)), "\n" for 1000000000000000000 .. 1000000000000000010;</syntaxhighlight>
{{out}}
<pre>1000000000000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
1000000000000000001 = 101 x 9901 x 999999000001
1000000000000000002 = 2 x 3 x 17 x 131 x 1427 x 52445056723
1000000000000000003 = 1000000000000000003
1000000000000000004 = 2 x 2 x 1801 x 246809 x 562425889
1000000000000000005 = 3 x 5 x 44087 x 691381 x 2187161
1000000000000000006 = 2 x 7 x 919 x 77724234416291
1000000000000000007 = 1370531 x 729644203597
1000000000000000008 = 2 x 2 x 2 x 3 x 3 x 97 x 26209 x 32779 x 166667
1000000000000000009 = 1000000000000000009
1000000000000000010 = 2 x 5 x 11 x 103 x 4013 x 21993833369</pre>
Giving similar output and also good for large inputs:
<syntaxhighlight lang="perl">use Math::Pari qw/factorint/;
sub factor {
my ($pn,$pc) = @{Math::Pari::factorint(shift)};
return map { ($pn->[$_]) x $pc->[$_] } 0 .. $#$pn;
}
print "$_ = ", join(" x ", factor($_)), "\n" for 1000000000000000000 .. 1000000000000000010;</syntaxhighlight>
or, somewhat slower and limited to native 32-bit or 64-bit integers only:
<syntaxhighlight lang="perl">use Math::Factor::XS qw/prime_factors/;
print "$_ = ", join(" x ", prime_factors($_)), "\n" for 1000000000000000000 .. 1000000000000000010;</syntaxhighlight>
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.
<syntaxhighlight lang="perl">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($_)), "\n" for 100000000000 .. 100000000100;</syntaxhighlight>
We could use the second extensible sieve from [[Sieve_of_Eratosthenes#Extensible_sieves]] to only divide by primes.
<syntaxhighlight lang="perl">tie my @primes, 'Tie::SieveOfEratosthenes';
sub factors {
my($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;</syntaxhighlight>
{{out}}
<pre>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</pre>
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 <code>map</code> to prefill the <tt>p_and_sq</tt> array.
<syntaxhighlight lang="perl">#!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?!";
}</syntaxhighlight>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">factorise</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">),</span><span style="color: #008000;">" x "</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)&{</span><span style="color: #000000;">2144</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1000000000</span><span style="color: #0000FF;">},</span><span style="color: #000000;">factorise</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
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
</pre>
=={{header|PicoLisp}}==
This is the 'factor' function from [[Prime decomposition#PicoLisp]].
<
(make
(let (D 2 L (1 2 2 . (4 2 4 2 4 6 2 6 .)) M (sqrt N))
Line 213 ⟶ 3,663:
(for N 20
(prinl N ": " (glue " * " (factor N))) )</
{{out}}
<pre>1: 1
2: 2
Line 235 ⟶ 3,685:
19: 19
20: 2 * 2 * 5</pre>
=={{header|PL/I}}==
<syntaxhighlight lang="pl/i">
cnt: procedure options (main);
declare (i, k, n) fixed binary;
declare first bit (1) aligned;
do n = 1 to 40;
put skip list (n || ' =');
k = n; first = '1'b;
repeat:
do i = 2 to k-1;
if mod(k, i) = 0 then
do;
k = k/i;
if ^first then put edit (' x ')(A);
first = '0'b;
put edit (trim(i)) (A);
go to repeat;
end;
end;
if ^first then put edit (' x ')(A);
if n = 1 then i = 1;
put edit (trim(i)) (A);
end;
end cnt;
</syntaxhighlight>
Results:
<pre> 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
</pre>
=={{header|PowerShell}}==
<syntaxhighlight lang="powershell">
function eratosthenes ($n) {
if($n -ge 1){
$prime = @(1..($n+1) | foreach{$true})
$prime[1] = $false
$m = [Math]::Floor([Math]::Sqrt($n))
for($i = 2; $i -le $m; $i++) {
if($prime[$i]) {
for($j = $i*$i; $j -le $n; $j += $i) {
$prime[$j] = $false
}
}
}
1..$n | where{$prime[$_]}
} else {
"$n must be equal or greater than 1"
}
}
function prime-decomposition ($n) {
$array = eratosthenes $n
$prime = @()
foreach($p in $array) {
while($n%$p -eq 0) {
$n /= $p
$prime += @($p)
}
}
$prime
}
$OFS = " x "
"$(prime-decomposition 2144)"
"$(prime-decomposition 100)"
"$(prime-decomposition 12)"
</syntaxhighlight>
<b>Output:</b>
<pre>
2 x 2 x 2 x 2 x 2 x 67
2 x 2 x 5 x 5
2 x 2 x 3
</pre>
=={{header|PureBasic}}==
<
Protected I = 3, Max
ClearList(Factors())
Line 274 ⟶ 3,836:
PrintN(text$)
Next a
EndIf</
{{out}}
<pre> 1= 1
2= 2
Line 296 ⟶ 3,859:
20= 2*2*5</pre>
=={{header|
This uses the [http://docs.python.org/dev/library/functools.html#functools.lru_cache functools.lru_cache] standard library module to cache intermediate results.
<syntaxhighlight lang="python">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())</syntaxhighlight>
{{out}}
<pre> 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)</pre>
=={{header|Quackery}}==
Reusing the code from [http://rosettacode.org/wiki/Prime_decomposition#Quackery Prime Decomposition].
<syntaxhighlight lang="quackery"> [ [] 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</syntaxhighlight>
{{out}}
<pre>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</pre>
… and so on. Quackery uses bignums, so "… until boredom ensues."
=={{header|R}}==
<syntaxhighlight lang="r">
#initially I created a function which returns prime factors then I have created another function counts in the factors and #prints the values.
findfactors <- function(num) {
x <- c()
p1<- 2
p2 <- 3
everyprime <- num
while( everyprime != 1 ) {
while( everyprime%%p1 == 0 ) {
x <- c(x, p1)
everyprime <- floor(everyprime/ p1)
}
p1 <- p2
p2 <- p2 + 2
}
x
}
count_in_factors=function(x){
primes=findfactors(x)
x=c(1)
for (i in 1:length(primes)) {
x=paste(primes[i],"x",x)
}
return(x)
}
count_in_factors(72)
</syntaxhighlight>
{{out}}
<pre>
[1] "3 x 3 x 2 x 2 x 2 x 1"
</pre>
=={{header|Racket}}==
See also [[#Scheme]]. This uses Racket’s <code>math/number-theory</code> package
<syntaxhighlight lang="racket">#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</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|rakudo|2015-10-01}}
<syntaxhighlight lang="raku" line>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($_).join(" × ") for 1..*;</syntaxhighlight>
The first twenty numbers:
<pre>1: 1
2: 2
3: 3
4: 2 × 2
5: 5
6: 2 × 3
7: 7
8: 2 × 2 × 2
9: 3 × 3
10: 2 × 5
11: 11
12: 2 × 2 × 3
13: 13
14: 2 × 7
15: 3 × 5
16: 2 × 2 × 2 × 2
17: 17
18: 2 × 3 × 3
19: 19
20: 2 × 2 × 5</pre>
Here we use a <tt>multi</tt> declaration with a constant parameter to match the degenerate case. We use <tt>copy</tt> parameters when we wish to reuse the formal parameter as a mutable variable within the function. (Parameters default to readonly in Raku.) Note the use of <tt>gather</tt>/<tt>take</tt> as the final statement in the function, which is a common Raku idiom to set up a coroutine within a function to return a lazy list on demand.
Note also the '×' above is not ASCII 'x', but U+00D7 MULTIPLICATION SIGN. Raku does Unicode natively.
Here is a solution inspired from [[Almost_prime#C]]. It doesn't use &is-prime.
<syntaxhighlight lang="raku" line>sub factor($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 $_ for 1 .. 20;</syntaxhighlight>
Same output as above.
Alternately, use a module:
<syntaxhighlight lang="raku" line>use Prime::Factor;
say "$_ = {(.&prime-factors || 1).join: ' x ' }" for flat 1 .. 10, 10**20 .. 10**20 + 10;</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|Refal}}==
<syntaxhighlight language="refal">$ENTRY Go {
= <Each Show <Iota 1 15> 2144>;
};
Factorize {
1 = 1;
s.N = <Factorize 2 s.N>;
s.D s.N, <Compare s.N s.D>: '-' = ;
s.D s.N, <Divmod s.N s.D>: {
(s.R) 0 = s.D <Factorize s.D s.R>;
e.X = <Factorize <+ 1 s.D> s.N>;
};
};
Join {
(e.J) = ;
(e.J) s.N = <Symb s.N>;
(e.J) s.N e.X = <Symb s.N> e.J <Join (e.J) e.X>;
};
Iota {
s.End s.End = s.End;
s.Start s.End = s.Start <Iota <+ s.Start 1> s.End>;
};
Each {
s.F = ;
s.F t.I e.X = <Mu s.F t.I> <Each s.F e.X>;
};
Show {
e.N = <Prout <Symb e.N> ' = ' <Join (' x ') <Factorize e.N>>>;
}; </syntaxhighlight>
{{out}}
<pre>1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
2144 = 2 x 2 x 2 x 2 x 2 x 67</pre>
=={{header|REXX}}==
===simple approach===
As per the task's requirements, the prime factors of '''1''' (unity) will be listed as '''1''',
<br>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
<br>prime factors are listed, but the number of primes found is always shown. The showing of the count of
<br>primes was included to help verify the factoring (of composites).
<syntaxhighlight lang="rexx">/*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. */</syntaxhighlight>
{{out|output|text= when using the default inputs:}}
<pre>
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.
</pre>
{{out|output|text= when the following input was used: <tt> 1 12 207820 </tt>}}
<pre>
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.
</pre>
{{out|output|text= when the following input was used: <tt> 1 -10000 </tt>}}
<pre>
1229 primes found.
</pre>
{{out|output|text= when the following input was used: <tt> 1 -100000 </tt>}}
<pre>
9592 primes found.
</pre>
===using integer SQRT===
This REXX version computes the ''integer square root'' of the integer being factor (to limit the range of factors),
<br>this makes this version about '''50%''' faster than the 1<sup>st</sup> 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.
<syntaxhighlight lang="rexx">/*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. */</syntaxhighlight>
{{out|output|text= when using the default inputs:}}
<pre>
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.
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="ring">
for i = 1 to 20
see "" + i + " = " + factors(i) + nl
next
func factors n
f = ""
if n = 1 return "1" ok
p = 2
while p <= n
if (n % p) = 0
f += string(p) + " x "
n = n/p
else p += 1 ok
end
return left(f, len(f) - 3)
</syntaxhighlight>
Output:
<pre>
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
</pre>
=={{header|RPL}}==
<code>PDIV</code> is defined at [[Prime decomposition#RPL|Prime decomposition]]
≪ { "1" } 2 ROT '''FOR''' j
"" j <span style="color:blue">PDIV</span> → factors
≪ '''IF''' factors SIZE 1 == '''THEN''' j →STR +
'''ELSE'''
1 factors SIZE '''FOR''' k
'''IF''' k 1 ≠ '''THEN''' 130 CHR + '''END'''
factors k GET →STR +
'''NEXT END'''
≫ + '''NEXT'''
≫ '<span style="color:blue">TASK</span>' STO
20 <span style="color:blue">TASK</span>
{{out}}
<pre>
1: { "1" "2" "3" "2×2" "5" "2×3" "7" "2×2×2" "3×3" "2×5" "11" "2×2×3" "13" "2×7" "3×5" "2×2×2×2" "17" "2×3×3" "19" "2×2×5" }
</pre>
=={{header|Ruby}}==
Starting with Ruby 1.9, 'prime' is part of the standard library and provides Integer#prime_division.
<syntaxhighlight lang="ruby">require 'optparse'
require 'prime'
Line 324 ⟶ 4,535:
end.join " x "
puts "#{i} is #{f}"
end</
{{out|Example}}
Usage: prime-count.rb [-m MAXIMUM]
-m MAXIMUM Count up to MAXIMUM [10]
$ ruby prime-count.rb -m 10000 |
1 is 1
2 is 2
Line 351 ⟶ 4,561:
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</pre>
=={{header|Run BASIC}}==
<syntaxhighlight lang="runbasic">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</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|Rust}}==
You can run and experiment with this code at https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=b66c14d944ff0472d2460796513929e2
<syntaxhighlight lang="rust">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]
}</syntaxhighlight>
{{out}}
<pre>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
</pre>
=={{header|Sage}}==
<syntaxhighlight lang="python">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("")</syntaxhighlight>
{{out}}
<pre>
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</pre>
=={{header|Scala}}==
<syntaxhighlight lang="scala">
object CountInFactors extends App {
def primeFactors(n: Int): List[Int] = {
def primeStream(s: LazyList[Int]): LazyList[Int] = {
s.head #:: primeStream(s.tail filter {
_ % s.head != 0
})
}
val primes = primeStream(LazyList.from(2))
def factors(n: Int): List[Int] = primes.takeWhile(_ <= n).find(n % _ == 0) match {
case None => Nil
case Some(p) => p :: factors(n / p)
}
if (n == 1) List(1) else factors(n)
}
// A little test...
{
val nums = (1 to 12).toList :+ 2144 :+ 6358
nums.foreach(n => println("%6d : %s".format(n, primeFactors(n).mkString(" * "))))
}
}
</syntaxhighlight>
{{out}}
<pre> 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</pre>
=={{header|Scheme}}==
<syntaxhighlight lang="lisp">(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))))</syntaxhighlight>
{{out}}
<pre>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
...</pre>
=={{header|Seed7}}==
<syntaxhighlight lang="seed7">$ include "seed7_05.s7i";
const proc: writePrimeFactors (in var integer: number) is func
local
var boolean: laterElement is FALSE;
var integer: checker is 2;
begin
while checker * checker <= number do
if number rem checker = 0 then
if laterElement then
write(" * ");
end if;
laterElement := TRUE;
write(checker);
number := number div checker;
else
incr(checker);
end if;
end while;
if number <> 1 then
if laterElement then
write(" * ");
end if;
laterElement := TRUE;
write(number);
end if;
end func;
const proc: main is func
local
var integer: number is 0;
begin
writeln("1: 1");
for number range 2 to 2147483647 do
write(number <& ": ");
writePrimeFactors(number);
writeln;
end for;
end func;</syntaxhighlight>
{{out}}
<pre>
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
. . .
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">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(' × ')}"
}</syntaxhighlight>
=={{header|Swift}}==
<syntaxhighlight lang="swift">extension BinaryInteger {
@inlinable
public func primeDecomposition() -> [Self] {
guard self > 1 else { return [] }
func step(_ x: Self) -> Self {
return 1 + (x << 2) - ((x >> 1) << 1)
}
let maxQ = Self(Double(self).squareRoot())
var d: Self = 1
var q: Self = self & 1 == 0 ? 2 : 3
while q <= maxQ && self % q != 0 {
q = step(d)
d += 1
}
return q <= maxQ ? [q] + (self / q).primeDecomposition() : [self]
}
}
for i in 1...20 {
if i == 1 {
print("1 = 1")
} else {
print("\(i) = \(i.primeDecomposition().map(String.init).joined(separator: " x "))")
}
}</syntaxhighlight>
{{out}}
<pre>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</pre>
=={{header|Tcl}}==
This factorization code is based on the same engine that is used in the [[Parallel calculations#Tcl|parallel computation task]].
<
namespace eval prime {
Line 415 ⟶ 5,035:
return [join $v "*"]
}
}</
Demonstration code:
<
for {set i 1} {$i <= $max} {incr i} {
puts [format "%*d = %s" [string length $max] $i [prime::factors.rendered $i]]
}</
=={{header|VBScript}}==
Made minor modifications on the code I posted under Prime Decomposition.
<syntaxhighlight lang="vb">Function CountFactors(n)
If n = 1 Then
CountFactors = 1
Else
arrP = Split(ListPrimes(n)," ")
Set arrList = CreateObject("System.Collections.ArrayList")
divnum = n
Do Until divnum = 1
'The -1 is to account for the null element of arrP
For i = 0 To UBound(arrP)-1
If divnum = 1 Then
Exit For
ElseIf divnum Mod arrP(i) = 0 Then
divnum = divnum/arrP(i)
arrList.Add arrP(i)
End If
Next
Loop
arrList.Sort
For i = 0 To arrList.Count - 1
If i = arrList.Count - 1 Then
CountFactors = CountFactors & arrList(i)
Else
CountFactors = CountFactors & arrList(i) & " * "
End If
Next
End If
End Function
Function IsPrime(n)
If n = 2 Then
IsPrime = True
ElseIf n <= 1 Or n Mod 2 = 0 Then
IsPrime = False
Else
IsPrime = True
For i = 3 To Int(Sqr(n)) Step 2
If n Mod i = 0 Then
IsPrime = False
Exit For
End If
Next
End If
End Function
Function ListPrimes(n)
ListPrimes = ""
For i = 1 To n
If IsPrime(i) Then
ListPrimes = ListPrimes & i & " "
End If
Next
End Function
'Testing the fucntions.
WScript.StdOut.Write "2 = " & CountFactors(2)
WScript.StdOut.WriteLine
WScript.StdOut.Write "2144 = " & CountFactors(2144)
WScript.StdOut.WriteLine</syntaxhighlight>
{{Out}}
<pre>
2 = 2
2144 = 2 * 2 * 2 * 2 * 2 * 67
</pre>
=={{header|Visual Basic .NET}}==
<
Sub Main()
Line 464 ⟶ 5,152:
End Sub
End Module</
{{out}}
<pre>
1 = 1
Line 488 ⟶ 5,176:
10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
</pre>
=={{header|V (Vlang)}}==
{{trans|go}}
<syntaxhighlight lang="v (vlang)">fn main() {
println("1: 1")
for i := 2; ; i++ {
print("$i: ")
mut x := ''
for n, f := i, 2; n != 1; f++ {
for m := n % f; m == 0; m = n % f {
print('$x$f')
x = "×"
n /= f
}
}
println('')
}
}</syntaxhighlight>
{{out}}
<pre>
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
...
</pre>
=={{header|Wren}}==
{{libheader|Wren-math}}
<syntaxhighlight lang="wren">import "./math" for Int
for (r in [1..9, 2144..2154, 9987..9999]) {
for (i in r) {
var factors = (i > 1) ? Int.primeFactors(i) : [1]
System.print("%(i): %(factors.join(" x "))")
}
System.print()
}</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">include c:\cxpl\codes;
int N0, N, F;
[N0:= 1;
repeat IntOut(0, N0); Text(0, " = ");
F:= 2; N:= N0;
repeat if rem(N/F) = 0 then
[if N # N0 then Text(0, " * ");
IntOut(0, F);
N:= N/F;
]
else F:= F+1;
until F>N;
if N0=1 then IntOut(0, 1); \1 = 1
CrLf(0);
N0:= N0+1;
until KeyHit;
]</syntaxhighlight>
Example output:
<pre>
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
</pre>
=={{header|zkl}}==
<syntaxhighlight lang="zkl">foreach n in ([1..*]){ println(n,": ",primeFactors(n).concat("\U2715;")) }</syntaxhighlight>
Using the fixed size integer (64 bit) solution from [[Prime decomposition#zkl]]
<syntaxhighlight lang="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;
}</syntaxhighlight>
{{out}}
<pre>
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
...
</pre>
=={{header|ZX Spectrum Basic}}==
{{trans|BBC_BASIC}}
<syntaxhighlight lang="zxbasic">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</syntaxhighlight>
| |||