# Factors of an integer

Factors of an integer
You are encouraged to solve this task according to the task description, using any language you may know.

Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.

You may see other such operations in the Basic Data Operations category, or:

Integer Operations
Arithmetic | Comparison

Boolean Operations
Bitwise | Logical

String Operations
Concatenation | Interpolation | Comparison | Matching

Memory Operations

Compute the   factors   of a positive integer.

These factors are the positive integers by which the number being factored can be divided to yield a positive integer result.

(Though the concepts function correctly for zero and negative integers, the set of factors of zero has countably infinite members, and the factors of negative integers can be obtained from the factors of related positive numbers without difficulty;   this task does not require handling of either of these cases).

Note that every prime number has two factors:   1   and itself.

## 0815

<:1:~>|~#:end:>~x}:str:/={^:wei:~%x<:a:x=~ =}:wei:x<:1:+{>~>x=-#:fin:^:str:}:fin:{{~% ## 11l Translation of: Python F factor(n) V factors = Set[Int]() L(x) 1..Int(sqrt(n)) I n % x == 0 factors.add(x) factors.add(n I/ x) R sorted(Array(factors)) L(i) (45, 53, 64) print(i‘: factors: ’String(factor(i))) Output: 45: factors: [1, 3, 5, 9, 15, 45] 53: factors: [1, 53] 64: factors: [1, 2, 4, 8, 16, 32, 64]  ## 360 Assembly Very compact version. * Factors of an integer - 07/10/2015 FACTOR CSECT USING FACTOR,R15 set base register LA R7,PG pgi=@pg LA R6,1 i L R3,N loop count LOOP L R5,N n LA R4,0 DR R4,R6 n/i LTR R4,R4 if mod(n,i)=0 BNZ NEXT XDECO R6,PG+120 edit i MVC 0(6,R7),PG+126 output i LA R7,6(R7) pgi=pgi+6 NEXT LA R6,1(R6) i=i+1 BCT R3,LOOP loop XPRNT PG,120 print buffer XR R15,R15 set return code BR R14 return to caller N DC F'12345' <== input value PG DC CL132' ' buffer YREGS END FACTOR Output:  1 3 5 15 823 2469 4115 12345  ## 68000 Assembly ;max input range equals 0 to 0xFFFFFFFF. jsr GetInput ;unimplemented routine to get user input for a positive (nonzero) integer. ;output of this routine will be in D0. MOVE.L D0,D1 ;D1 will be used for temp storage. MOVE.L #1,D2 ;start with 1. computeFactors: DIVU D2,D1 ;remainder is in top 2 bytes, quotient in bottom 2. MOVE.L D1,D3 ;temporarily store into D3 to check the remainder SWAP D3 ;swap the high and low words of D3. Now bottom 2 bytes contain remainder. CMP.W #0,D3 ;is the bottom word equal to 0? BNE D2_Wasnt_A_Divisor ;if not, D2 was not a factor of D1. JSR PrintD2 ;unimplemented routine to print D2 to the screen as a decimal number. D2_Wasnt_A_Divisor: MOVE.L D0,D1 ;restore D1. ADDQ.L #1,D2 ;increment D2 CMP.L D2,D1 ;is D2 now greater than D1? BLS computeFactors ;if not, loop again ;end of program  ## AArch64 Assembly Works with: as version Raspberry Pi 3B version Buster 64 bits /* ARM assembly AARCH64 Raspberry PI 3B */ /* program factorst64.s */ /*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly*/ .include "../includeConstantesARM64.inc" .equ CHARPOS, '@' /*******************************************/ /* Initialized data */ /*******************************************/ .data szMessDeb: .ascii "Factors of : @ are : \n" szMessFactor: .asciz "@ \n" szCarriageReturn: .asciz "\n" /*******************************************/ /* UnInitialized data */ /*******************************************/ .bss sZoneConversion: .skip 100 /*******************************************/ /* code section */ /*******************************************/ .text .global main main: // entry of program mov x0,#100 bl factors mov x0,#97 bl factors ldr x0,qNumber bl factors 100: // standard end of the program mov x0, #0 // return code mov x8, #EXIT // request to exit program svc 0 // perform the system call qNumber: .quad 32767 qAdrszCarriageReturn: .quad szCarriageReturn /******************************************************************/ /* calcul factors of number */ /******************************************************************/ /* x0 contains the number to factorize */ factors: stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers mov x5,x0 // limit calcul ldr x1,qAdrsZoneConversion // conversion register in decimal string bl conversion10S ldr x0,qAdrszMessDeb // display message ldr x1,qAdrsZoneConversion bl strInsertAtChar bl affichageMess mov x6,#1 // counter loop 1: // loop udiv x0,x5,x6 // division msub x3,x0,x6,x5 // compute remainder cbnz x3,2f // remainder not = zero -> loop // display result if yes mov x0,x6 ldr x1,qAdrsZoneConversion bl conversion10S ldr x0,qAdrszMessFactor // display message ldr x1,qAdrsZoneConversion bl strInsertAtChar bl affichageMess 2: add x6,x6,#1 // add 1 to loop counter cmp x6,x5 // <= number ? ble 1b // yes loop 100: ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret qAdrszMessDeb: .quad szMessDeb qAdrszMessFactor: .quad szMessFactor qAdrsZoneConversion: .quad sZoneConversion /******************************************************************/ /* insert string at character insertion */ /******************************************************************/ /* x0 contains the address of string 1 */ /* x1 contains the address of insertion string */ /* x0 return the address of new string on the heap */ /* or -1 if error */ strInsertAtChar: stp x2,lr,[sp,-16]! // save registers stp x3,x4,[sp,-16]! // save registers stp x5,x6,[sp,-16]! // save registers stp x7,x8,[sp,-16]! // save registers mov x3,#0 // length counter 1: // compute length of string 1 ldrb w4,[x0,x3] cmp w4,#0 cinc x3,x3,ne // increment to one if not equal bne 1b // loop if not equal mov x5,#0 // length counter insertion string 2: // compute length to insertion string ldrb w4,[x1,x5] cmp x4,#0 cinc x5,x5,ne // increment to one if not equal bne 2b // and loop cmp x5,#0 beq 99f // string empty -> error add x3,x3,x5 // add 2 length add x3,x3,#1 // +1 for final zero mov x6,x0 // save address string 1 mov x0,#0 // allocation place heap mov x8,BRK // call system 'brk' svc #0 mov x5,x0 // save address heap for output string add x0,x0,x3 // reservation place x3 length mov x8,BRK // call system 'brk' svc #0 cmp x0,#-1 // allocation error beq 99f mov x2,0 mov x4,0 3: // loop copy string begin ldrb w3,[x6,x2] cmp w3,0 beq 99f cmp w3,CHARPOS // insertion character ? beq 5f // yes strb w3,[x5,x4] // no store character in output string add x2,x2,1 add x4,x4,1 b 3b // and loop 5: // x4 contains position insertion add x8,x4,1 // init index character output string // at position insertion + one mov x3,#0 // index load characters insertion string 6: ldrb w0,[x1,x3] // load characters insertion string cmp w0,#0 // end string ? beq 7f // yes strb w0,[x5,x4] // store in output string add x3,x3,#1 // increment index add x4,x4,#1 // increment output index b 6b // and loop 7: // loop copy end string ldrb w0,[x6,x8] // load other character string 1 strb w0,[x5,x4] // store in output string cmp x0,#0 // end string 1 ? beq 8f // yes -> end add x4,x4,#1 // increment output index add x8,x8,#1 // increment index b 7b // and loop 8: mov x0,x5 // return output string address b 100f 99: // error mov x0,#-1 100: ldp x7,x8,[sp],16 // restaur 2 registers ldp x5,x6,[sp],16 // restaur 2 registers ldp x3,x4,[sp],16 // restaur 2 registers ldp x2,lr,[sp],16 // restaur 2 registers ret /********************************************************/ /* File Include fonctions */ /********************************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeARM64.inc" ## ACL2 (defun factors-r (n i) (declare (xargs :measure (nfix (- n i)))) (cond ((zp (- n i)) (list n)) ((= (mod n i) 0) (cons i (factors-r n (1+ i)))) (t (factors-r n (1+ i))))) (defun factors (n) (factors-r n 1))  ## Action! PROC PrintFactors(CARD a) BYTE notFirst CARD p p=1 notFirst=0 WHILE p<=a DO IF a MOD p=0 THEN IF notFirst THEN Print(", ") FI notFirst=1 PrintC(p) FI p==+1 OD RETURN PROC Test(CARD a) PrintF("Factors of %U: ",a) PrintFactors(a) PutE() RETURN PROC Main() Test(1) Test(101) Test(666) Test(1977) Test(2021) Test(6502) Test(12345) RETURN Output: Factors of 1: 1 Factors of 101: 1, 101 Factors of 666: 1, 2, 3, 6, 9, 18, 37,74, 111, 222, 333, 666 Factors of 1977: 1, 3, 659, 1977 Factors of 2021: 1, 43, 47, 2021 Factors of 6502: 1, 2, 3251, 6502 Factors of 12345: 1, 3, 5, 15, 823, 2469, 4115, 12345  ## ActionScript function factor(n:uint):Vector.<uint> { var factors:Vector.<uint> = new Vector.<uint>(); for(var i:uint = 1; i <= n; i++) if(n % i == 0)factors.push(i); return factors; }  ## Ada with Ada.Text_IO; with Ada.Command_Line; procedure Factors is Number : Positive; Test_Nr : Positive := 1; begin if Ada.Command_Line.Argument_Count /= 1 then Ada.Text_IO.Put (Ada.Text_IO.Standard_Error, "Missing argument!"); Ada.Command_Line.Set_Exit_Status (Ada.Command_Line.Failure); return; end if; Number := Positive'Value (Ada.Command_Line.Argument (1)); Ada.Text_IO.Put ("Factors of" & Positive'Image (Number) & ": "); loop if Number mod Test_Nr = 0 then Ada.Text_IO.Put (Positive'Image (Test_Nr) & ","); end if; exit when Test_Nr ** 2 >= Number; Test_Nr := Test_Nr + 1; end loop; Ada.Text_IO.Put_Line (Positive'Image (Number) & "."); end Factors;  ## Aikido import math function factor (n:int) { var result = [] function append (v) { if (!(v in result)) { result.append (v) } } var sqrt = cast<int>(Math.sqrt (n)) append (1) for (var i = n-1 ; i >= sqrt ; i--) { if ((n % i) == 0) { append (i) append (n/i) } } append (n) return result.sort() } function printvec (vec) { var comma = "" print ("[") foreach v vec { print (comma + v) comma = ", " } println ("]") } printvec (factor (45)) printvec (factor (25)) printvec (factor (100)) ## ALGOL 68 Works with: ALGOL 68 version Revision 1 - no extensions to language used Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d Note: The following implements generators, eliminating the need of declaring arbitrarily long int arrays for caching. MODE YIELDINT = PROC(INT)VOID; PROC gen factors = (INT n, YIELDINT yield)VOID: ( FOR i FROM 1 TO ENTIER sqrt(n) DO IF n MOD i = 0 THEN yield(i); INT other = n OVER i; IF i NE other THEN yield(n OVER i) FI FI OD ); []INT nums2factor = (45, 53, 64); FOR i TO UPB nums2factor DO INT num = nums2factor[i]; STRING sep := ": "; print(num); # FOR INT j IN # gen factors(num, # ) DO ( # ## (INT j)VOID:( print((sep,whole(j,0))); sep:=", " # OD # )); print(new line) OD Output:  +45: 1, 45, 3, 15, 5, 9 +53: 1, 53 +64: 1, 64, 2, 32, 4, 16, 8  ## ALGOL W begin % return the factors of n ( n should be >= 1 ) in the array factor % % the bounds of factor should be 0 :: len (len must be at least 1) % % the number of factors will be returned in factor( 0 ) % procedure getFactorsOf ( integer value n ; integer array factor( * ) ; integer value len ) ; begin for i := 0 until len do factor( i ) := 0; if n >= 1 and len >= 1 then begin integer pos, lastFactor; factor( 0 ) := factor( 1 ) := pos := 1; % find the factors up to sqrt( n ) % for f := 2 until truncate( sqrt( n ) ) + 1 do begin if ( n rem f ) = 0 and pos <= len then begin % found another factor and there's room to store it % pos := pos + 1; factor( 0 ) := pos; factor( pos ) := f end if_found_factor end for_f; % find the factors above sqrt( n ) % lastFactor := factor( factor( 0 ) ); for f := factor( 0 ) step -1 until 1 do begin integer newFactor; newFactor := n div factor( f ); if newFactor > lastFactor and pos <= len then begin % found another factor and there's room to store it % pos := pos + 1; factor( 0 ) := pos; factor( pos ) := newFactor end if_found_factor end for_f; end if_params_ok end getFactorsOf ; % prpocedure to test getFactorsOf % procedure testFactorsOf( integer value n ) ; begin integer array factor( 0 :: 100 ); getFactorsOf( n, factor, 100 ); i_w := 1; s_w := 0; % set output format % write( n, " has ", factor( 0 ), " factors:" ); for f := 1 until factor( 0 ) do writeon( " ", factor( f ) ) end testFactorsOf ; % test the factorising % for i := 1 until 100 do testFactorsOf( i ) end. Output: 1 has 1 factors: 1 2 has 2 factors: 1 2 3 has 2 factors: 1 3 4 has 3 factors: 1 2 4 ... 96 has 12 factors: 1 2 3 4 6 8 12 16 24 32 48 96 97 has 2 factors: 1 97 98 has 6 factors: 1 2 7 14 49 98 99 has 6 factors: 1 3 9 11 33 99 100 has 9 factors: 1 2 4 5 10 20 25 50 100  ## ALGOL-M Instead of displaying 1 and the number itself as factors, prime numbers are explicitly reported as such. To reduce the number of test divisions, only odd divisors are tested if an initial check shows the number to be factored is not even. The upper limit of divisors is set at N/2 or N/3, depending on whether N is even or odd, and is continuously reduced to N divided by the next potential divisor until the first factor is found. For a prime number the resulting limit will be the square root of N, which avoids the necessity of explicitly calculating that value. (ALGOL-M does not have a built-in square root function.) BEGIN COMMENT RETURN P MOD Q; INTEGER FUNCTION MOD (P, Q); INTEGER P, Q; BEGIN MOD := P - Q * (P / Q); END; INTEGER I, N, LIMIT, FOUND, START, DELTA; WHILE 1 = 1 DO BEGIN WRITE ("NUMBER TO FACTOR (OR 0 TO QUIT):"); READ (N); IF N = 0 THEN GOTO DONE; WRITE ("THE FACTORS ARE:"); COMMENT CHECK WHETHER NUMBER IS EVEN OR ODD; IF MOD(N, 2) = 0 THEN BEGIN START := 2; DELTA := 1; END ELSE BEGIN START := 3; DELTA := 2; END; COMMENT TEST POTENTIAL DIVISORS; FOUND := 0; I := START; LIMIT := N / I; WHILE I <= LIMIT DO BEGIN IF MOD(N, I) = 0 THEN BEGIN WRITEON (I); FOUND := FOUND + 1; END; I := I + DELTA; IF FOUND = 0 THEN LIMIT := N / I; END; IF FOUND = 0 THEN WRITEON (" NONE - THE NUMBER IS PRIME."); WRITE(""); END; DONE: WRITE ("GOODBYE"); END Output: NUMBER TO FACTOR (OR 0 TO QUIT): -> 96 THE FACTORS ARE: 2 3 4 6 8 12 16 24 32 48 NUMBER TO FACTOR (OR 0 TO QUIT): -> 97 THE FACTORS ARE: NONE - THE NUMBER IS PRIME. NUMBER TO FACTOR (OR 0 TO QUIT): -> 98 THE FACTORS ARE: 2 7 14 49 NUMBER TO FACTOR (OR 0 TO QUIT): -> 0 GOODBYE ## APL  factors←{(0=(⍳⍵)|⍵)/⍳⍵} factors 12345 1 3 5 15 823 2469 4115 12345 factors 720 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720  ## AppleScript ### Functional Translation of: JavaScript -- integerFactors :: Int -> [Int] on integerFactors(n) if n = 1 then {1} else if 1 > n then missing value else set realRoot to n ^ (1 / 2) set intRoot to realRoot as integer set blnPerfectSquare to intRoot = realRoot -- isFactor :: Int -> Bool script isFactor on |λ|(x) (n mod x) = 0 end |λ| end script -- Factors up to square root of n, set lows to filter(isFactor, enumFromTo(1, intRoot)) -- integerQuotient :: Int -> Int script integerQuotient on |λ|(x) (n / x) as integer end |λ| end script -- and quotients of these factors beyond the square root. lows & map(integerQuotient, ¬ items (1 + (blnPerfectSquare as integer)) thru -1 of reverse of lows) end if end integerFactors --------------------------- TEST ------------------------- on run integerFactors(120) --> {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120} end run -------------------- GENERIC FUNCTIONS ------------------- -- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n) if n < m then set d to -1 else set d to 1 end if set lst to {} repeat with i from m to n by d set end of lst to i end repeat return lst end enumFromTo -- filter :: (a -> Bool) -> [a] -> [a] on filter(f, xs) tell mReturn(f) set lst to {} set lng to length of xs repeat with i from 1 to lng set v to item i of xs if |λ|(v, i, xs) then set end of lst to v end repeat return lst end tell end filter -- map :: (a -> b) -> [a] -> [b] on map(f, xs) tell mReturn(f) set lng to length of xs set lst to {} repeat with i from 1 to lng set end of lst to |λ|(item i of xs, i, xs) end repeat return lst end tell end map -- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f) if class of f is script then f else script property |λ| : f end script end if end mReturn  Output: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}  ### Straightforward on factors(n) set output to {} set sqrt to n ^ 0.5 set limit to sqrt div 1 if (limit = sqrt) then set end of output to limit set limit to limit - 1 end if repeat with i from limit to 1 by -1 if (n mod i is 0) then set beginning of output to i set end of output to n div i end if end repeat return output end factors factors(123456789)  Output: {1, 3, 9, 3607, 3803, 10821, 11409, 32463, 34227, 13717421, 41152263, 123456789}  ## Arc (= divisor (fn (num) (= dlist '()) (when (is 1 num) (= dlist '(1 0))) (when (is 2 num) (= dlist '(2 1))) (unless (or (is 1 num) (is 2 num)) (up i 1 (+ 1 (/ num 2)) (if (is 0 (mod num i)) (push i dlist))) (= dlist (cons num dlist))) dlist)) (map [rev _] (map [divisor _] '(45 53 60 64))) Output: '( (1 3 5 9 15 45) (1 53) (1 2 3 4 5 6 10 12 15 20 30 60) (1 2 4 8 16 32 64) ) ## ARM Assembly Works with: as version Raspberry Pi /* ARM assembly Raspberry PI */ /* program factorst.s */ /* Constantes */ .equ STDOUT, 1 @ Linux output console .equ EXIT, 1 @ Linux syscall .equ WRITE, 4 @ Linux syscall /* Initialized data */ .data szMessDeb: .ascii "Factors of :" sMessValeur: .fill 12, 1, ' ' .asciz "are : \n" sMessFactor: .fill 12, 1, ' ' .asciz "\n" szCarriageReturn: .asciz "\n" /* UnInitialized data */ .bss /* code section */ .text .global main main: /* entry of program */ push {fp,lr} /* saves 2 registers */ mov r0,#100 bl factors mov r0,#97 bl factors ldr r0,iNumber bl factors 100: /* standard end of the program */ mov r0, #0 @ return code pop {fp,lr} @restaur 2 registers mov r7, #EXIT @ request to exit program swi 0 @ perform the system call iNumber: .int 32767 iAdrszCarriageReturn: .int szCarriageReturn /******************************************************************/ /* calcul factors of number */ /******************************************************************/ /* r0 contains the number */ factors: push {fp,lr} /* save registres */ push {r1-r6} /* save others registers */ mov r5,r0 @ limit calcul ldr r1,iAdrsMessValeur @ conversion register in decimal string bl conversion10S ldr r0,iAdrszMessDeb @ display message bl affichageMess mov r6,#1 @ counter loop 1: @ loop mov r0,r5 @ dividende mov r1,r6 @ divisor bl division cmp r3,#0 @ remainder = zero ? bne 2f @ display result if yes mov r0,r6 ldr r1,iAdrsMessFactor bl conversion10S ldr r0,iAdrsMessFactor bl affichageMess 2: add r6,#1 @ add 1 to loop counter cmp r6,r5 @ <= number ? ble 1b @ yes loop 100: pop {r1-r6} /* restaur others registers */ pop {fp,lr} /* restaur des 2 registres */ bx lr /* return */ iAdrsMessValeur: .int sMessValeur iAdrszMessDeb: .int szMessDeb iAdrsMessFactor: .int sMessFactor /******************************************************************/ /* display text with size calculation */ /******************************************************************/ /* r0 contains the address of the message */ affichageMess: push {fp,lr} /* save registres */ push {r0,r1,r2,r7} /* save others registers */ mov r2,#0 /* counter length */ 1: /* loop length calculation */ ldrb r1,[r0,r2] /* read octet start position + index */ cmp r1,#0 /* if 0 its over */ addne r2,r2,#1 /* else add 1 in the length */ bne 1b /* and loop */ /* so here r2 contains the length of the message */ mov r1,r0 /* address message in r1 */ mov r0,#STDOUT /* code to write to the standard output Linux */ mov r7, #WRITE /* code call system "write" */ swi #0 /* call systeme */ pop {r0,r1,r2,r7} /* restaur others registers */ pop {fp,lr} /* restaur des 2 registres */ bx lr /* return */ /*=============================================*/ /* division integer unsigned */ /*============================================*/ division: /* r0 contains N */ /* r1 contains D */ /* r2 contains Q */ /* r3 contains R */ push {r4, lr} mov r2, #0 /* r2 ? 0 */ mov r3, #0 /* r3 ? 0 */ mov r4, #32 /* r4 ? 32 */ b 2f 1: movs r0, r0, LSL #1 /* r0 ? r0 << 1 updating cpsr (sets C if 31st bit of r0 was 1) */ adc r3, r3, r3 /* r3 ? r3 + r3 + C. This is equivalent to r3 ? (r3 << 1) + C */ cmp r3, r1 /* compute r3 - r1 and update cpsr */ subhs r3, r3, r1 /* if r3 >= r1 (C=1) then r3 ? r3 - r1 */ adc r2, r2, r2 /* r2 ? r2 + r2 + C. This is equivalent to r2 ? (r2 << 1) + C */ 2: subs r4, r4, #1 /* r4 ? r4 - 1 */ bpl 1b /* if r4 >= 0 (N=0) then branch to .Lloop1 */ pop {r4, lr} bx lr /***************************************************/ /* conversion register in string décimal signed */ /***************************************************/ /* r0 contains the register */ /* r1 contains address of conversion area */ conversion10S: push {fp,lr} /* save registers frame and return */ push {r0-r5} /* save other registers */ mov r2,r1 /* early storage area */ mov r5,#'+' /* default sign is + */ cmp r0,#0 /* négatif number ? */ movlt r5,#'-' /* yes sign is - */ mvnlt r0,r0 /* and inverse in positive value */ addlt r0,#1 mov r4,#10 /* area length */ 1: /* conversion loop */ bl divisionpar10 /* division */ add r1,#48 /* add 48 at remainder for conversion ascii */ strb r1,[r2,r4] /* store byte area r5 + position r4 */ sub r4,r4,#1 /* previous position */ cmp r0,#0 bne 1b /* loop if quotient not equal zéro */ strb r5,[r2,r4] /* store sign at current position */ subs r4,r4,#1 /* previous position */ blt 100f /* if r4 < 0 end */ /* else complete area with space */ mov r3,#' ' /* character space */ 2: strb r3,[r2,r4] /* store byte */ subs r4,r4,#1 /* previous position */ bge 2b /* loop if r4 greather or equal zero */ 100: /* standard end of function */ pop {r0-r5} /*restaur others registers */ pop {fp,lr} /* restaur des 2 registers frame et return */ bx lr /***************************************************/ /* division par 10 signé */ /* Thanks to http://thinkingeek.com/arm-assembler-raspberry-pi/* /* and http://www.hackersdelight.org/ */ /***************************************************/ /* r0 contient le dividende */ /* r0 retourne le quotient */ /* r1 retourne le reste */ divisionpar10: /* r0 contains the argument to be divided by 10 */ push {r2-r4} /* save autres registres */ mov r4,r0 ldr r3, .Ls_magic_number_10 /* r1 <- magic_number */ smull r1, r2, r3, r0 /* r1 <- Lower32Bits(r1*r0). r2 <- Upper32Bits(r1*r0) */ mov r2, r2, ASR #2 /* r2 <- r2 >> 2 */ mov r1, r0, LSR #31 /* r1 <- r0 >> 31 */ add r0, r2, r1 /* r0 <- r2 + r1 */ add r2,r0,r0, lsl #2 /* r2 <- r0 * 5 */ sub r1,r4,r2, lsl #1 /* r1 <- r4 - (r2 * 2) = r4 - (r0 * 10) */ pop {r2-r4} bx lr /* leave function */ .align 4 .Ls_magic_number_10: .word 0x66666667 ## Arturo factors:[num][
select 1..num [x][
(num%x)=0
]
]

print factors 36

Output:
1 2 3 4 6 9 12 18 36

## Asymptote

int[] n = {11, 21, 32, 45, 67, 519};

for(var j : n) {
write(j, suffix=none);
write(" =>", suffix=none);
for(int i = 1; i < (j/2); ++i) {
if(j % i == 0) {
write(" ", i, suffix=none);
}
}
write(" ", j);
}

Output:
11 => 1 11
21 => 1 3 7 21
32 => 1 2 4 8 32
45 => 1 3 5 9 15 45
67 => 1 67
519 => 1 3 173 519

## AutoHotkey

msgbox, % factors(45) "n" factors(53) "n" factors(64)

Factors(n)
{  Loop, % floor(sqrt(n))
{  v := A_Index = 1 ? 1 "," n : mod(n,A_Index) ? v : v "," A_Index "," n//A_Index
}
Sort, v, N U D,
Return, v
}

Output:
1,3,5,9,15,45
1,53
1,2,4,8,16,32,64

## AutoIt

;AutoIt Version: 3.2.10.0
$num = 45 MsgBox (0,"Factors", "Factors of " &$num & " are: " & factors($num)) consolewrite ("Factors of " &$num & " are: " & factors($num)) Func factors($intg)
$ls_factors="" For$i = 1 to $intg/2 if ($intg/$i - int($intg/$i))=0 Then$ls_factors=$ls_factors&$i &", "
EndIf
Next
Return $ls_factors&$intg
EndFunc

Output:
Factors of 45 are: 1, 3, 5, 9, 15, 45


## AWK

# syntax: GAWK -f FACTORS_OF_AN_INTEGER.AWK
BEGIN {
print("enter a number or C/R to exit")
}
{   if ($0 == "") { exit(0) } if ($0 !~ /^[0-9]+$/) { printf("invalid: %s\n",$0)
next
}
n = $0 printf("factors of %s:",n) for (i=1; i<=n; i++) { if (n % i == 0) { printf(" %d",i) } } printf("\n") }  Output: enter a number or C/R to exit invalid: -1 factors of 0: factors of 1: 1 factors of 2: 1 2 factors of 11: 1 11 factors of 64: 1 2 4 8 16 32 64 factors of 100: 1 2 4 5 10 20 25 50 100 factors of 32766: 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766 factors of 32767: 1 7 31 151 217 1057 4681 32767  ## BASIC Works with: QBasic This example stores the factors in a shared array (with the original number as the last element) for later retrieval. Note that this will error out if you pass 32767 (or higher). DECLARE SUB factor (what AS INTEGER) REDIM SHARED factors(0) AS INTEGER DIM i AS INTEGER, L AS INTEGER INPUT "Gimme a number"; i factor i PRINT factors(0); FOR L = 1 TO UBOUND(factors) PRINT ","; factors(L); NEXT PRINT SUB factor (what AS INTEGER) DIM tmpint1 AS INTEGER DIM L0 AS INTEGER, L1 AS INTEGER REDIM tmp(0) AS INTEGER REDIM factors(0) AS INTEGER factors(0) = 1 FOR L0 = 2 TO what IF (0 = (what MOD L0)) THEN 'all this REDIMing and copying can be replaced with: 'REDIM PRESERVE factors(UBOUND(factors)+1) 'in languages that support the PRESERVE keyword REDIM tmp(UBOUND(factors)) AS INTEGER FOR L1 = 0 TO UBOUND(factors) tmp(L1) = factors(L1) NEXT REDIM factors(UBOUND(factors) + 1) FOR L1 = 0 TO UBOUND(factors) - 1 factors(L1) = tmp(L1) NEXT factors(UBOUND(factors)) = L0 END IF NEXT END SUB  Output:  Gimme a number? 17 1 , 17 Gimme a number? 12345 1 , 3 , 5 , 15 , 823 , 2469 , 4115 , 12345 Gimme a number? 32765 1 , 5 , 6553 , 32765 Gimme a number? 32766 1 , 2 , 3 , 6 , 43 , 86 , 127 , 129 , 254 , 258 , 381 , 762 , 5461 , 10922 , 16383 , 32766  ### Applesoft BASIC The Factors_of_an_integer#Sinclair ZX81 BASIC code works the same in Applesoft BASIC. ### ASIC Translation of: GW-BASIC REM Factors of an integer PRINT "Enter an integer"; LOOP: INPUT N IF N = 0 THEN LOOP: NA = ABS(N) NDIV2 = NA / 2 FOR I = 1 TO NDIV2 NMODI = NA MOD I IF NMODI = 0 THEN PRINT I; ENDIF NEXT I PRINT NA END  Output: Enter an integer?60 1 2 3 4 5 6 10 12 15 20 30 60  ### BASIC256 Translation of: FreeBASIC subroutine printFactors(n) print n; " => "; for i = 1 to n / 2 if n mod i = 0 then print i; " "; next i print n end subroutine call printFactors(11) call printFactors(21) call printFactors(32) call printFactors(45) call printFactors(67) call printFactors(96) end Output: Igual que la entrada de FreeBASIC.  ### GW-BASIC 10 INPUT "Enter an integer: ", N 20 IF N = 0 THEN GOTO 10 30 NA = ABS(N) 40 FOR I = 1 TO NA/2 50 IF NA MOD I = 0 THEN PRINT I; 60 NEXT I 70 PRINT NA  Output: Enter an integer: 1 1 Enter an integer: 12 1 2 3 4 6 12 Enter an integer: 13 1 13 Enter an integer: -22222 1 2 41 82 271 542 11111 22222  ### IS-BASIC 100 PROGRAM "Factors.bas" 110 INPUT PROMPT "Number: ":N 120 FOR I=1 TO INT(N/2) 130 IF MOD(N,I)=0 THEN PRINT I; 140 NEXT 150 PRINT N ### Minimal BASIC Translation of: GW-BASIC Works with: Commodore BASIC Works with: Nascom ROM BASIC version 4.7 10 REM Factors of an integer 20 PRINT "Enter an integer"; 30 INPUT N 40 IF N = 0 THEN 30 50 N1 = ABS(N) 60 FOR I = 1 TO N1/2 70 IF INT(N1/I)*I <> N1 THEN 90 80 PRINT I; 90 NEXT I 100 PRINT N1 110 END  ### Nascom BASIC Translation of: GW-BASIC Works with: Nascom ROM BASIC version 4.7 10 REM Factors of an integer 20 INPUT "Enter an integer"; N 30 IF N=0 THEN 20 40 NA=ABS(N) 50 FOR I=1 TO INT(NA/2) 60 IF NA=INT(NA/I)*I THEN PRINT I; 70 NEXT I 80 PRINT NA 90 END  Output: Enter an integer? 60 1 2 3 4 5 6 10 12 15 20 30 60  See also Minimal BASIC ### Sinclair ZX81 BASIC Works with: Applesoft BASIC 10 INPUT N 20 FOR I=1 TO N 30 IF N/I=INT (N/I) THEN PRINT I;" "; 40 NEXT I  Input: 315 Output: 1 3 5 7 9 15 35 45 63 105 315 ### Tiny BASIC 100 PRINT "Give me a number:" 110 INPUT I 120 LET C=1 130 PRINT "Factors of ",I,":" 140 IF I/C*C=I THEN PRINT C 150 LET C=C+1 160 IF C<=I THEN GOTO 140 170 END Output: Give me a number: 60 Factors of 60: 1 2 3 4 5 6 10 12 15 20 30 60  ### True BASIC Translation of: FreeBASIC sub printfactors(n) if n < 1 then exit sub print n; "=>"; for i = 1 to n / 2 if remainder(n, i) = 0 then print i; next i print n end sub call printfactors(11) call printfactors(21) call printfactors(32) call printfactors(45) call printfactors(67) call printfactors(96) print end  Output: Igual que la entrada de FreeBASIC.  ## Batch File Command line version: @echo off set res=Factors of %1: for /L %%i in (1,1,%1) do call :fac %1 %%i echo %res% goto :eof :fac set /a test = %1 %% %2 if %test% equ 0 set res=%res% %2  Output: >factors 32767 Factors of 32767: 1 7 31 151 217 1057 4681 32767 >factors 45 Factors of 45: 1 3 5 9 15 45 >factors 53 Factors of 53: 1 53 >factors 64 Factors of 64: 1 2 4 8 16 32 64 >factors 100 Factors of 100: 1 2 4 5 10 20 25 50 100 Interactive version: @echo off set /p limit=Gimme a number: set res=Factors of %limit%: for /L %%i in (1,1,%limit%) do call :fac %limit% %%i echo %res% goto :eof :fac set /a test = %1 %% %2 if %test% equ 0 set res=%res% %2  Output: >factors Gimme a number:27 Factors of 27: 1 3 9 27 >factors Gimme a number:102 Factors of 102: 1 2 3 6 17 34 51 102 ## BBC BASIC  INSTALL @lib$+"SORTLIB"
sort% = FN_sortinit(0, 0)

PRINT "The factors of 45 are " FNfactorlist(45)
PRINT "The factors of 12345 are " FNfactorlist(12345)
END

DEF FNfactorlist(N%)
LOCAL C%, I%, L%(), L$DIM L%(32) FOR I% = 1 TO SQR(N%) IF (N% MOD I% = 0) THEN L%(C%) = I% C% += 1 IF (N% <> I%^2) THEN L%(C%) = (N% DIV I%) C% += 1 ENDIF ENDIF NEXT I% CALL sort%, L%(0) FOR I% = 0 TO C%-1 L$ += STR$(L%(I%)) + ", " NEXT = LEFT$(LEFT$(L$))

Output:
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345

## bc

/* Calculate the factors of n and return their count.
* This function mutates the global array f[] which will
* contain all factors of n in ascending order after the call!
*/
define f(n) {
auto i, d, h, h[], l, o
/* Local variables:
* i: Loop variable.
* d: Complementary (higher) factor to i.
* h: Will always point to the last element of h[].
* h[]: Array to hold the greater factor of the pair (x, y), where
*      x * y == n. The factors are stored in descending order.
* l: Will always point to the next free spot in f[].
* o: For saving the value of scale.
*/

/* Use integer arithmetic */
o = scale
scale = 0

/* Two factors are 1 and n (if n != 1) */
f[l++] = 1
if (n == 1) return(1)
h[0] = n

/* Main loop */
for (i = 2; i < h[h]; i++) {
if (n % i == 0) {
d = n / i
if (d != i) {
h[++h] = d
}
f[l++] = i
}
}

/* Append the values in h[] to f[] */
while (h >= 0) {
f[l++] = h[h--]
}

scale = o
return(l)
}


## Befunge

10:p&v:      >:0:g%#v_0:g\:0:g/\v
>:0:g:*|      >           >0:g1+0:p
>:0:g:*-#v_0:g\>$>:!#@_.v > ^ ^ ," "<  ## BQN A bqncrate idiom. Factors ← (1+↕)⊸(⊣/˜0=|) •Show Factors 12345 •Show Factors 729 ⟨ 1 3 5 15 823 2469 4115 12345 ⟩ ⟨ 1 3 9 27 81 243 729 ⟩  The primes library from bqn-libs can be used for a solution that's more efficient for large inputs. FactorExponents returns each unique prime factor along with its exponent. ⟨FactorExponents⟩ ← •Import "primes.bqn" # With appropriate path Factors ← { ∧⥊ 1 ×⌜´ ⋆⟜(↕1+⊢)¨˝ FactorExponents 𝕩 } ## Burlesque blsq ) 32767 fc {1 7 31 151 217 1057 4681 32767} ## C #include <stdio.h> #include <stdlib.h> typedef struct { int *list; short count; } Factors; void xferFactors( Factors *fctrs, int *flist, int flix ) { int ix, ij; int newSize = fctrs->count + flix; if (newSize > flix) { fctrs->list = realloc( fctrs->list, newSize * sizeof(int)); } else { fctrs->list = malloc( newSize * sizeof(int)); } for (ij=0,ix=fctrs->count; ix<newSize; ij++,ix++) { fctrs->list[ix] = flist[ij]; } fctrs->count = newSize; } Factors *factor( int num, Factors *fctrs) { int flist[301], flix; int dvsr; flix = 0; fctrs->count = 0; free(fctrs->list); fctrs->list = NULL; for (dvsr=1; dvsr*dvsr < num; dvsr++) { if (num % dvsr != 0) continue; if ( flix == 300) { xferFactors( fctrs, flist, flix ); flix = 0; } flist[flix++] = dvsr; flist[flix++] = num/dvsr; } if (dvsr*dvsr == num) flist[flix++] = dvsr; if (flix > 0) xferFactors( fctrs, flist, flix ); return fctrs; } int main(int argc, char*argv[]) { int nums2factor[] = { 2059, 223092870, 3135, 45 }; Factors ftors = { NULL, 0}; char sep; int i,j; for (i=0; i<4; i++) { factor( nums2factor[i], &ftors ); printf("\nfactors of %d are:\n ", nums2factor[i]); sep = ' '; for (j=0; j<ftors.count; j++) { printf("%c %d", sep, ftors.list[j]); sep = ','; } printf("\n"); } return 0; }  ### Prime factoring #include <stdio.h> #include <stdlib.h> #include <string.h> /* 65536 = 2^16, so we can factor all 32 bit ints */ char bits[65536]; typedef unsigned long ulong; ulong primes[7000], n_primes; typedef struct { ulong p, e; } prime_factor; /* prime, exponent */ void sieve() { int i, j; memset(bits, 1, 65536); bits[0] = bits[1] = 0; for (i = 0; i < 256; i++) if (bits[i]) for (j = i * i; j < 65536; j += i) bits[j] = 0; /* collect primes into a list. slightly faster this way if dealing with large numbers */ for (i = j = 0; i < 65536; i++) if (bits[i]) primes[j++] = i; n_primes = j; } int get_prime_factors(ulong n, prime_factor *lst) { ulong i, e, p; int len = 0; for (i = 0; i < n_primes; i++) { p = primes[i]; if (p * p > n) break; for (e = 0; !(n % p); n /= p, e++); if (e) { lst[len].p = p; lst[len++].e = e; } } return n == 1 ? len : (lst[len].p = n, lst[len].e = 1, ++len); } int ulong_cmp(const void *a, const void *b) { return *(const ulong*)a < *(const ulong*)b ? -1 : *(const ulong*)a > *(const ulong*)b; } int get_factors(ulong n, ulong *lst) { int n_f, len, len2, i, j, k, p; prime_factor f[100]; n_f = get_prime_factors(n, f); len2 = len = lst[0] = 1; /* L = (1); L = (L, L * p**(1 .. e)) forall((p, e)) */ for (i = 0; i < n_f; i++, len2 = len) for (j = 0, p = f[i].p; j < f[i].e; j++, p *= f[i].p) for (k = 0; k < len2; k++) lst[len++] = lst[k] * p; qsort(lst, len, sizeof(ulong), ulong_cmp); return len; } int main() { ulong fac[10000]; int len, i, j; ulong nums[] = {3, 120, 1024, 2UL*2*2*2*3*3*3*5*5*7*11*13*17*19 }; sieve(); for (i = 0; i < 4; i++) { len = get_factors(nums[i], fac); printf("%lu:", nums[i]); for (j = 0; j < len; j++) printf(" %lu", fac[j]); printf("\n"); } return 0; }  Output: 3: 1 3 120: 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 1024: 1 2 4 8 16 32 64 128 256 512 1024 3491888400: 1 2 3 4 5 6 7 8 9 10 11 ...(>1900 numbers)... 1163962800 1745944200 3491888400 ## C# ### C# 1.0 static void Main (string[] args) { do { Console.WriteLine ("Number:"); Int64 p = 0; do { try { p = Convert.ToInt64 (Console.ReadLine ()); break; } catch (Exception) { } } while (true); Console.WriteLine ("For 1 through " + ((int) Math.Sqrt (p)).ToString () + ""); for (int x = 1; x <= (int) Math.Sqrt (p); x++) { if (p % x == 0) Console.WriteLine ("Found: " + x.ToString () + ". " + p.ToString () + " / " + x.ToString () + " = " + (p / x).ToString ()); } Console.WriteLine ("Done."); } while (true); }  ### C# 3.0 using System; using System.Collections.Generic; using System.Linq; public static class Extension { public static List<int> Factors (this int me) { return Enumerable.Range (1, me).Where (x => me % x == 0).ToList (); } } class Program { static void Main (string[] args) { Console.WriteLine (String.Join (", ", 45. Factors ())); } }  Output: Number: 32434243 For 1 through 5695 Found: 1. 32434243 / 1 = 32434243 Found: 307. 32434243 / 307 = 105649 Done. ## C++ #include <iostream> #include <iomanip> #include <vector> #include <algorithm> #include <iterator> std::vector<int> GenerateFactors(int n) { std::vector<int> factors = { 1, n }; for (int i = 2; i * i <= n; ++i) { if (n % i == 0) { factors.push_back(i); if (i * i != n) factors.push_back(n / i); } } std::sort(factors.begin(), factors.end()); return factors; } int main() { const int SampleNumbers[] = { 3135, 45, 60, 81 }; for (size_t i = 0; i < sizeof(SampleNumbers) / sizeof(int); ++i) { std::vector<int> factors = GenerateFactors(SampleNumbers[i]); std::cout << "Factors of "; std::cout.width(4); std::cout << SampleNumbers[i] << " are: "; std::copy(factors.begin(), factors.end(), std::ostream_iterator<int>(std::cout, " ")); std::cout << std::endl; } return EXIT_SUCCESS; }  Output: Factors of 3135 are: 1 3 5 11 15 19 33 55 57 95 165 209 285 627 1045 3135 Factors of 45 are: 1 3 5 9 15 45 Factors of 60 are: 1 2 3 4 5 6 10 12 15 20 30 60 Factors of 81 are: 1 3 9 27 81  ## Ceylon shared void run() { {Integer*} getFactors(Integer n) => (1..n).filter((Integer element) => element.divides(n)); for(Integer i in 1..100) { print("the factors of i are getFactors(i)"); } }  ## Chapel Inspired by the Clojure solution: iter factors(n) { for i in 1..floor(sqrt(n)):int { if n % i == 0 then { yield i; yield n / i; } } }  ## Clojure (defn factors [n] (filter #(zero? (rem n %)) (range 1 (inc n)))) (print (factors 45))  (1 3 5 9 15 45)  Improved version. Considers small factors from 1 up to (sqrt n) -- we increment it because range does not include the end point. Pair each small factor with its co-factor, flattening the results, and put them into a sorted set to get the factors in order. (defn factors [n] (into (sorted-set) (mapcat (fn [x] [x (/ n x)]) (filter #(zero? (rem n %)) (range 1 (inc (Math/sqrt n)))) )))  Same idea, using for comprehensions. (defn factors [n] (into (sorted-set) (reduce concat (for [x (range 1 (inc (Math/sqrt n))) :when (zero? (rem n x))] [x (/ n x)]))))  ## CLU Translation of: Sather isqrt = proc (s: int) returns (int) x0: int := s/2 if x0=0 then return(s) end x1: int := (x0 + s/x0)/2 while x1<x0 do x0, x1 := x1, (x1 + s/x1)/2 end return(x0) end isqrt factors = iter (n: int) yields (int) yield(1) for i: int in int$from_to(2,isqrt(n)) do
if n//i=0 then
yield(i)
if i*i ~= n then yield(n/i) end
end
end
yield(n)
end factors

start_up = proc ()
po: stream := stream$primary_output() a: array[int] := array[int]$[3135, 45, 64, 53, 45, 81]
for n: int in array[int]$elements(a) do stream$puts(po, "Factors of " || int$unparse(n) || ":") for f: int in factors(n) do stream$puts(po, " " || int$unparse(f)) end stream$putl(po, "")
end
end start_up
Output:
Factors of 3135: 1 3 1045 5 627 11 285 15 209 19 165 33 95 55 57 3135
Factors of 45: 1 3 15 5 9 45
Factors of 64: 1 2 32 4 16 8 64
Factors of 53: 1 53
Factors of 45: 1 3 15 5 9 45
Factors of 81: 1 3 27 9 81

## COBOL

       IDENTIFICATION DIVISION.
PROGRAM-ID. FACTORS.
DATA DIVISION.
WORKING-STORAGE SECTION.
01  CALCULATING.
03  NUM  USAGE BINARY-LONG VALUE ZERO.
03  LIM  USAGE BINARY-LONG VALUE ZERO.
03  CNT  USAGE BINARY-LONG VALUE ZERO.
03  DIV  USAGE BINARY-LONG VALUE ZERO.
03  REM  USAGE BINARY-LONG VALUE ZERO.
03  ZRS  USAGE BINARY-SHORT VALUE ZERO.

01  DISPLAYING.
03  DIS  PIC 9(10) USAGE DISPLAY.

PROCEDURE DIVISION.
MAIN-PROCEDURE.
DISPLAY "Factors of? " WITH NO ADVANCING
ACCEPT NUM
DIVIDE NUM BY 2 GIVING LIM.

PERFORM VARYING CNT FROM 1 BY 1 UNTIL CNT > LIM
DIVIDE NUM BY CNT GIVING DIV REMAINDER REM
IF REM = 0
MOVE CNT TO DIS
PERFORM SHODIS
END-IF
END-PERFORM.

MOVE NUM TO DIS.
PERFORM SHODIS.
STOP RUN.

SHODIS.
MOVE ZERO TO ZRS.
INSPECT DIS TALLYING ZRS FOR LEADING ZERO.
DISPLAY DIS(ZRS + 1:)
EXIT PARAGRAPH.

END PROGRAM FACTORS.


## CoffeeScript

# Reference implementation for finding factors is slow, but hopefully
# robust--we'll use it to verify the more complicated (but hopefully faster)
# algorithm.
slow_factors = (n) ->
(i for i in [1..n] when n % i == 0)

# The rest of this code does two optimizations:
#   1) When you find a prime factor, divide it out of n (smallest_prime_factor).
#   2) Find the prime factorization first, then compute composite factors from those.

smallest_prime_factor = (n) ->
for i in [2..n]
return n if i*i > n
return i if n % i == 0

prime_factors = (n) ->
return {} if n == 1
spf = smallest_prime_factor n
result = prime_factors(n / spf)
result[spf] or= 0
result[spf] += 1
result

fast_factors = (n) ->
prime_hash = prime_factors n
exponents = []
for p of prime_hash
exponents.push
p: p
exp: 0
result = []
while true
factor = 1
for obj in exponents
factor *= Math.pow obj.p, obj.exp
result.push factor
break if factor == n
# roll the odometer
for obj, i in exponents
if obj.exp < prime_hash[obj.p]
obj.exp += 1
break
else
obj.exp = 0

return result.sort (a, b) -> a - b

verify_factors = (factors, n) ->
expected_result = slow_factors n
throw Error("wrong length") if factors.length != expected_result.length
for factor, i in expected_result
console.log Error("wrong value") if factors[i] != factor

for n in [1, 3, 4, 8, 24, 37, 1001, 11111111111, 99999999999]
factors = fast_factors n
console.log n, factors
if n < 1000000
verify_factors factors, n

Output:
> coffee factors.coffee
1 [ 1 ]
3 [ 1, 3 ]
4 [ 1, 2, 4 ]
8 [ 1, 2, 4, 8 ]
24 [ 1, 2, 3, 4, 6, 8, 12, 24 ]
37 [ 1, 37 ]
1001 [ 1, 7, 11, 13, 77, 91, 143, 1001 ]
11111111111 [ 1, 21649, 513239, 11111111111 ]
99999999999 [ 1,
3,
9,
21649,
64947,
194841,
513239,
1539717,
4619151,
11111111111,
33333333333,
99999999999 ]

## Common Lisp

We iterate in the range 1..sqrt(n) collecting ‘low’ factors and corresponding ‘high’ factors, and combine at the end to produce an ordered list of factors.

(defun factors (n &aux (lows '()) (highs '()))
(do ((limit (1+ (isqrt n))) (factor 1 (1+ factor)))
((= factor limit)
(when (= n (* limit limit))
(push limit highs))
(remove-duplicates (nreconc lows highs)))
(multiple-value-bind (quotient remainder) (floor n factor)
(when (zerop remainder)
(push factor lows)
(push quotient highs)))))


## Crystal

Translation of: Ruby

Brute force and slow, by checking every value up to n.

struct Int
def factors() (1..self).select { |n| (self % n).zero? } end
end


Faster, by only checking values up to ${\displaystyle \sqrt{n}}$.

struct Int
def factors
f = [] of Int32
(1..Math.sqrt(self)).each{ |i|
(f << i; f << self // i if self // i != i) if (self % i).zero?
}
f.sort
end
end


Tests:

[45, 53, 64].each {|n| puts "#{n} : #{n.factors}"}

Output:
45 : [1, 3, 5, 9, 15, 45]
53 : [1, 53]
64 : [1, 2, 4, 8, 16, 32, 64]

## D

### Procedural Style

import std.stdio, std.math, std.algorithm;

T[] factors(T)(in T n) pure nothrow {
if (n == 1)
return [n];

T[] res = [1, n];
T limit = cast(T)real(n).sqrt + 1;
for (T i = 2; i < limit; i++) {
if (n % i == 0) {
res ~= i;
immutable q = n / i;
if (q > i)
res ~= q;
}
}

return res.sort().release;
}

void main() {
writefln("%(%s\n%)", [45, 53, 64, 1111111].map!factors);
}

Output:
[1, 3, 5, 9, 15, 45]
[1, 53]
[1, 2, 4, 8, 16, 32, 64]
[1, 239, 4649, 1111111]

### Functional Style

import std.stdio, std.algorithm, std.range;

auto factors(I)(I n) {
return iota(1, n + 1).filter!(i => n % i == 0);
}

void main() {
36.factors.writeln;
}

Output:
[1, 2, 3, 4, 6, 9, 12, 18, 36]

## Dart

import 'dart:math';

factors(n)
{
var factorsArr = [];
for(var test = n - 1; test >= sqrt(n).toInt(); test--)
if(n % test == 0)
{
}
return factorsArr;
}

void main() {
print(factors(5688));
}


## Dc

### Simple O(n) version

[Enter positive number: ]P ? sn
[Factors of ]P lnn [ are: ]P
[q]sq 1si [[ ]P lin]sp [ li ln <q ln li % 0=p li1+si lxx ]dsxx AP
Output:
Factors of 998877 are:  1 3 11 33 30269 90807 332959 998877
0m1.120s


### Faster O(sqrt(n)) version

[Enter positive number: ]P ? sn
[Factors of ]P lnn [ are: ]P
[q]sq lnvsv 1si 0sj [[ ]P lin]sp [lkSb lj1+sj]sa [lpx ln li /dsk li<a ]sP
[li lv <q ln li % 0=P li1+si lxx]dsxx
[lj 1>q lj1-sj Lbsi lpx lxx]dsxx AP
0m0.004s


See #Pascal.

## Dyalect

func Iterator.Where(pred) {
for x in this when pred(x) {
yield x
}
}

func Integer.Factors() {
(1..this).Where(x => this % x == 0)
}

for x in 45.Factors() {
print(x)
}

Output:

1
3
5
9
15
45

## E

 This example is in need of improvement: Use a cleverer algorithm such as in the Common Lisp example.
def factors(x :(int > 0)) {
var xfactors := []
for f ? (x % f <=> 0) in 1..x {
xfactors with= f
}
return xfactors
}

## EasyLang

n = 720
for i = 1 to n
if n mod i = 0
factors[] &= i
.
.
print factors[]


## EchoLisp

prime-factors gives the list of n's prime-factors. We mix them to get all the factors.

;; ppows
;; input : a list g of grouped prime factors ( 3 3 3 ..)
;; returns (1 3 9 27 ...)

(define (ppows g (mult 1))
(for/fold (ppows '(1)) ((a g))
(set! mult (* mult a))
(cons mult ppows)))

;; factors
;; decomp n into ((2 2 ..) ( 3 3 ..)  ) prime factors groups
;; combines (1 2 4 8 ..) (1 3 9 ..) lists

(define (factors n)
(list-sort <
(if (<= n 1) '(1)
(for/fold (divs'(1)) ((g (map  ppows (group (prime-factors n)))))
(for*/list ((a divs) (b g)) (* a b))))))

Output:
(lib 'bigint)
(factors 666)
→ (1 2 3 6 9 18 37 74 111 222 333 666)

(length (factors 108233175859200))
→ 666 ;; 💀

(define huge 1200034005600070000008900000000000000000)
(time ( length (factors huge)))
→ (394ms 7776)


## EDSAC order code

Input is limited to 10 decimal digits, which is as many as the EDSAC print subroutine P7 can handle. Factors are printed in pairs, such that the product of the factors in each pair equals the input number.

2021-10-10 Integers are now read from the tape in decimal format, instead of being defined by the awkward method of pseudo-orders. The factorization of 999,999,999 has been removed, as it took too long on the commonly-used EdsacPC simulator (14.6 million orders - over 6 hours on the original EDSAC).

  [Factors of an integer, from Rosetta Code website.]
[EDSAC program, Initial Orders 2.]

[The numbers to  be factorized are read in by library subroutine R2
(Wilkes, Wheeler and Gill, 1951 edition, pp.96-97, 148).]
[The address of the integers is placed in location 46, so they can be
referred to by the N parameter (or we could have used 45 and H, etc.)]
T   46 K
P  600 F  [address of integers]
[Subroutine R2]
GKT20FVDL8FA40DUDTFI40FA40FS39FG@S2FG23FA5@T5@E4@E13Z
T     #N  [pass address of integers to R2]

[List of integers to be factorized; edit ad lib. R2 requires 'F' after
each integer except the last, and '#' (pi) after the last.
This program uses 0 to mark the end of the list.]
42000F999999F0#

[Modified library subroutine P7.]
[Prints signed integer; up to 10 digits, left-justified.]
[Input: 0D = integer,]
T   56 K
TFH17@S17@A43@G23@UFS43@T1FV4DAFG50@SFLDUFXFOFFFSFL4FT4DA49@
T31@A1FA43@G20@XFP1024FP610D@524D!FO46@O26@XFSFL8FT4DE39@

[Division subroutine for positive long integers.
35-bit dividend and divisor (max 2^34 - 1)
returning quotient and remainder.
Input:  dividend at 4D, divisor at 6D
Output: remainder at 4D, quotient at 6D.
37 locations; working locations 0D, 8D.]
T  110 K

[Subroutine to find and print factors of a positive integer.
Input: 0D = integer, maximum 10 decimal digits.
T  148 K
G      K
A    3 F  [form and plant link for return]
T   55 @
A      D [load integer whose factors are to be found]
T   56#@ [store]
T   58#@ [possible factor := 1]
S   65 @ [negative count of items per line]
T   64 @ [initialize count]

[Start of loop round possible factors]
[8]   T      F [clear acc]
T    4 D [to 4F for division]
T    6 D [to 6F for division]
A   13 @ [for return from next]
G  110 F [do division; clears acc]
A    6 D [save quotient (6F may be changed below)]
T   60#@
S    4 D [load negative of remainder]
G   44 @ [skip if remainder > 0]

[Here if m is a factor of n.]
[Print m and the quotient together]
T      F [clear acc]
A   64 @ [test count of items per line]
G   26 @ [skip if not start of line]
S   65 @ [start of line, reset count]
T   64 @
O   70 @ [and print CR, LF]
O   71 @
[26]   T      F [clear acc]
O   67 @ [print '(']
T      D [to 0D for printing]
A   30 @ [for return from next]
G   56 F [print factor; clears acc]
O   69 @ [print comma]
T      D [to 0D for printing]
A   35 @ [for return from next]
G   56 F [print quotient; clears acc]
O   68 @ [print ')']
A   64 @ [negative counter for items per line]
A    2 F [inc]
E   43 @ [skip if end of line]
O   66 @ [not end of line, print 2 spaces]
O   66 @
[43]   T   64 @ [update counter]

[Common code after testing possible factor]
[44]   T      F [clear acc]
A   62#@ [inc by 1]
U   58#@ [store back]
S   60#@ [compare with quotient]
G    8 @ [loop if (new factor) < (old quotient)]

[Here when found all factors]
O   70 @ [print CR, LF twice]
O   71 @
O   70 @
O   71 @
T      F [exit with acc = 0]
[55]   E      F [return]
[--------]
[56]   PF    PF [number whose factors are to be found]
[58]   PF    PF [possible factor]
[60]   PF    PF [integer part of (number/factor)]
T62#Z PF [clear sandwich digit in 35-bit constant 1]
[62]   PD    PF [35-bit constant 1]
[64]   P      F [negative counter for items per line]
[65]   P    4 F [items per line, in address field]
[66]   !      F [space]
[67]   K      F [left parenthesis (in figures mode)]
[68]   L      F [right parenthesis (in figures mode)]
[69]   N      F [comma (in figures mode)]
[70]   @      F [carriage return]
[71]   &      F [line feed]

[Main routine for demonstrating subroutine.]
T  400 K
G      K
[0]   #      F [set figures mode]
[1]   K 4096 F [null char]
[2]   S     #N [order to load negative of first number]
[3]   P    2 F [to inc address by 2 for next number]

[Enter with acc = 0]
[4]   O      @ [set teleprinter to figures]
A    2 @ [load order for first integer]
[6]   T    7 @ [plant in next order]
[7]   S      D [load negative of 35-bit integer]
E   17 @ [exit if number is 0]
T      D [negative to 0D]
S      D [convert to positive]
T      D [pass to subroutine]
A   12 @ [call subroutine to find and print factors]
G  148 F
A    7 @ [modify order above, for next integer]
A    3 @
E    6 @ [always jump, since S = 12 > 0]
[--------]
[17]   O    1 @ [done, print null to flush printer buffer]
Z      F [stop]

E    4 Z  [define entry point]
P      F  [acc = 0 on entry]
Output:
(1,42000)  (2,21000)  (3,14000)  (4,10500)
(5,8400)  (6,7000)  (7,6000)  (8,5250)
(10,4200)  (12,3500)  (14,3000)  (15,2800)
(16,2625)  (20,2100)  (21,2000)  (24,1750)
(25,1680)  (28,1500)  (30,1400)  (35,1200)
(40,1050)  (42,1000)  (48,875)  (50,840)
(56,750)  (60,700)  (70,600)  (75,560)
(80,525)  (84,500)  (100,420)  (105,400)
(112,375)  (120,350)  (125,336)  (140,300)
(150,280)  (168,250)  (175,240)  (200,210)

(1,999999)  (3,333333)  (7,142857)  (9,111111)
(11,90909)  (13,76923)  (21,47619)  (27,37037)
(33,30303)  (37,27027)  (39,25641)  (63,15873)
(77,12987)  (91,10989)  (99,10101)  (111,9009)
(117,8547)  (143,6993)  (189,5291)  (231,4329)
(259,3861)  (273,3663)  (297,3367)  (333,3003)
(351,2849)  (407,2457)  (429,2331)  (481,2079)
(693,1443)  (777,1287)  (819,1221)  (999,1001)


## Ela

### Using higher-order function

open list

factors m = filter (\x -> m % x == 0) [1..m]

### Using comprehension

factors m = [x \\ x <- [1..m] | m % x == 0]

## Elixir

defmodule RC do
def factor(1), do: [1]
def factor(n) do
(for i <- 1..div(n,2), rem(n,i)==0, do: i) ++ [n]
end

# Recursive (faster version);
def divisor(n), do: divisor(n, 1, []) |> Enum.sort

defp divisor(n, i, factors) when n < i*i    , do: factors
defp divisor(n, i, factors) when n == i*i   , do: [i | factors]
defp divisor(n, i, factors) when rem(n,i)==0, do: divisor(n, i+1, [i, div(n,i) | factors])
defp divisor(n, i, factors)                 , do: divisor(n, i+1, factors)
end

Enum.each([45, 53, 60, 64], fn n ->
IO.puts "#{n}: #{inspect RC.factor(n)}"
end)

IO.puts "\nRange: #{inspect range = 1..10000}"
funs = [ factor:  &RC.factor/1,
divisor: &RC.divisor/1 ]
Enum.each(funs, fn {name, fun} ->
{time, value} = :timer.tc(fn -> Enum.count(range, &length(fun.(&1))==2) end)
IO.puts "#{name}\t prime count : #{value},\t#{time/1000000} sec"
end)

Output:
45: [1, 3, 5, 9, 15, 45]
53: [1, 53]
60: [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]
64: [1, 2, 4, 8, 16, 32, 64]

Range: 1..10000
factor   prime count : 1229,    7.316 sec
divisor  prime count : 1229,    0.265 sec


## Erlang

### with Built in fuctions

factors(N) ->
[I || I <- lists:seq(1,trunc(N/2)), N rem I == 0]++[N].


### Recursive

Another, less concise, but faster version

-module(divs).
-export([divs/1]).

divs(0) -> [];
divs(1) -> [];
divs(N) -> lists:sort(divisors(1,N))++[N].

divisors(1,N) ->
[1] ++ divisors(2,N,math:sqrt(N)).

divisors(K,_N,Q) when K > Q -> [];
divisors(K,N,_Q) when N rem K =/= 0 ->
[] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) when K * K  == N ->
[K] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) ->
[K, N div K] ++ divisors(K+1,N,math:sqrt(N)).

Output:
58> timer:tc(divs, factors, [20000]).
{2237,
[1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,
500,625,800,1000,1250,2000,2500,4000|...]}
59> timer:tc(divs, divs, [20000]).
{106,
[1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,
500,625,800,1000,1250,2000,2500,4000|...]}


The first number is milliseconds. I'v ommitted repeating the first fuction.

## ERRE

PROGRAM FACTORS

!$DOUBLE PROCEDURE FACTORLIST(N->L$)

LOCAL C%,I,FLIPS%,I%
LOCAL DIM L[32]
FOR I=1 TO SQR(N) DO
IF N=I*INT(N/I) THEN
L[C%]=I
C%=C%+1
IF N<>I*I THEN
L[C%]=INT(N/I)
C%=C%+1
END IF
END IF
END FOR

! BUBBLE SORT ARRAY L[]
FLIPS%=1
WHILE FLIPS%>0 DO
FLIPS%=0
FOR I%=0 TO C%-2 DO
IF L[I%]>L[I%+1] THEN SWAP(L[I%],L[I%+1]) FLIPS%=1
END FOR
END WHILE

L$="" FOR I%=0 TO C%-1 DO L$=L$+STR$(L[I%])+","
END FOR
L$=LEFT$(L$,LEN(L$)-1)

END PROCEDURE

BEGIN
PRINT(CHR$(12);) ! CLS FACTORLIST(45->L$)
PRINT("The factors of 45 are ";L$) FACTORLIST(12345->L$)
PRINT("The factors of 12345 are ";L$) END PROGRAM Output: The factors of 45 are 1, 3, 5, 9, 15, 45 The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345  ## Excel ### LAMBDA Binding the name FACTORS to a custom function defined by the following LAMBDA expression in the Name Manager of an Excel workbook. =LAMBDA(n, IF(1 < n, LET( froot, SQRT(n), nroot, FLOOR.MATH(froot), lows, FILTERP( LAMBDA(x, 0 = MOD(n, x)) )( ENUMFROMTO(1)(nroot) ), APPEND(lows)( LAMBDA(x, n / x)( REVERSE( IF(froot <> nroot, lows, INIT(lows) ) ) ) ) ), IF(1 = n, {1}, NA()) ) )  and assuming that in the same worksheet, each of the following names is bound to the reusable generic lambda expression which follows it: APPEND =LAMBDA(xs, LAMBDA(ys, LET( nx, ROWS(xs), rowIndexes, SEQUENCE(nx + ROWS(ys)), colIndexes, SEQUENCE( 1, MAX(COLUMNS(xs), COLUMNS(ys)) ), IF( rowIndexes <= nx, INDEX(xs, rowIndexes, colIndexes), INDEX(ys, rowIndexes - nx, colIndexes) ) ) ) ) ENUMFROMTO =LAMBDA(a, LAMBDA(z, SEQUENCE(1 + z - a, 1, a, 1) ) ) FILTERP =LAMBDA(p, LAMBDA(xs, FILTER(xs, p(xs)) ) ) INIT =LAMBDA(xs, IF( AND(1=ROWS(xs), ISBLANK(xs)), NA(), INDEX( xs, SEQUENCE(ROWS(xs)-1, 1, 1, 1) ) ) ) REVERSE =LAMBDA(xs, LET( n, ROWS(xs), SORTBY( xs, SEQUENCE(n, 1, n, -1) ) ) )  The FACTORS function, applied to an integer, defines a column of integer values. Here we define a row instead, by composing FACTORS with the standard TRANSPOSE function. Output:  =TRANSPOSE(FACTORS(A2)) fx A B C D E F G H I J K L M N O P Q 1 N Factors 2 64 1 2 4 8 16 32 64 3 120 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 4 123456789 1 3 9 3607 3803 10821 11409 32463 34227 13717421 41152263 123456789 5 2 1 2 6 1 1 7 0 #N/A 8 -1 #N/A ## F# If number % divisor = 0 then both divisor AND number / divisor are factors. So, we only have to search till sqrt(number). Also, this is lazily evaluated. let factors number = seq { for divisor in 1 .. (float >> sqrt >> int) number do if number % divisor = 0 then yield divisor if number <> 1 then yield number / divisor //special case condition: when number=1 then divisor=(number/divisor), so don't repeat it }  ### Prime factoring [6;120;2048;402642;1206432] |> Seq.iter(fun n->printf "%d :" n; [1..n]|>Seq.filter(fun g->n%g=0)|>Seq.iter(fun n->printf " %d" n); printfn "");;  Output: OUTPUT : 6 : 1 2 3 6 120 : 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 2048 : 1 2 4 8 16 32 64 128 256 512 1024 2048 402642 : 1 2 3 6 9 18 22369 44738 67107 134214 201321 402642 120643200 : 1 2 3 4 6 8 9 12 16 18 24 32 36 48 59 71 72 96 118 142 144 177 213 236 284 288 354 426 472 531 568 639 708 852 944 1062 1136 12 78 1416 1704 1888 2124 2272 2556 2832 3408 4189 4248 5112 5664 6816 8378 8496 10224 12567 16756 16992 20448 25134 33512 37701 50268 67024 75402 10053 6 134048 150804 201072 301608 402144 603216 1206432  ## Factor  USE: math.primes.factors ( scratchpad ) 24 divisors . { 1 2 3 4 6 8 12 24 }  ## FALSE [1[\$@$@-][\$@$@$@$@\/*=[$." "]?1+]#.%]f:
45f;! 53f;! 64f;!

## Fish

0v
>i:0(?v'0'%+a*
>~a,:1:>r{%        ?vr:nr','ov
^:&:;?(&:+1r:<        <


Must be called with pre-polulated value (Positive Integer) in the input stack. Try at Fish Playground[1].

For Input Number :
 120

The following output was generated:

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120,

## Forth

This is a slightly optimized algorithm, since it realizes there are no factors between n/2 and n. The values are saved on the stack and - in true Forth fashion - printed in descending order.

: factors dup 2/ 1+ 1 do dup i mod 0= if i swap then loop ;
: .factors factors begin dup dup . 1 <> while drop repeat drop cr ;

45 .factors
53 .factors
64 .factors
100 .factors


### Alternative version with vectored execution

It's not really idiomatic FORTH to leave a variable number of items on the stack, so instead this version repeatedly calls an execution token for each factor, and it uses a defining word to create a fold over the factors of an integer. This version also only tests up to the square root, which means that items are generated in pairs, rather than in sorted order.

: sq  s" dup *" evaluate ; immediate

: factors ( n a xt -- )
swap 2>r 1
BEGIN 2dup sq > WHILE
2dup /mod swap 0= IF
over
r> r@ execute
r@ execute >r
ELSE
drop
THEN 1+
REPEAT
2dup sq = IF
2r> swap execute nip
ELSE
2drop r> rdrop
THEN ;

: <with-factors>
create 2, does> 2@ factors ;

0 :noname nip 1+ ; <with-factors> count-factors
0 ' + <with-factors> sum-factors

0 :noname swap . ; <with-factors> (.factors)
: .factors  (.factors) drop ;

Output:
100 .factors 1 100 2 50 4 25 5 20 10  ok
100 count-factors . 9  ok
100 sum-factors . 217  ok
1 100 + 2 + 50 + 4 + 25 + 5 + 20 + 10 + . 217  ok  \ test sum-factors result
77 .factors 1 77 7 11  ok
108 .factors 1 108 2 54 3 36 4 27 6 18 9 12  ok


## Fortran

Works with: Fortran version 90 and later
program Factors
implicit none
integer :: i, number

write(*,*) "Enter a number between 1 and 2147483647"

do i = 1, int(sqrt(real(number))) - 1
if (mod(number, i) == 0) write (*,*) i, number/i
end do

! Check to see if number is a square
i = int(sqrt(real(number)))
if (i*i == number) then
write (*,*) i
else if (mod(number, i) == 0) then
write (*,*) i, number/i
end if

end program


## FreeBASIC

' FB 1.05.0 Win64

Sub printFactors(n As Integer)
If n < 1 Then Return
Print n; " =>";
For i As Integer = 1 To n / 2
If n Mod i = 0 Then Print i; " ";
Next i
Print n
End Sub

printFactors(11)
printFactors(21)
printFactors(32)
printFactors(45)
printFactors(67)
printFactors(96)
Print
Print "Press any key to quit"
Sleep

Output:
 11 => 1  11
21 => 1  3  7  21
32 => 1  2  4  8  16  32
45 => 1  3  5  9  15  45
67 => 1  67
96 => 1  2  3  4  6  8  12  16  24  32  48  96


## Frink

Frink has built-in factoring functions which use wheel factoring, trial division, Pollard p-1 factoring, and Pollard rho factoring. It also recognizes some special forms (e.g. Mersenne numbers) and handles them efficiently. Integers can either be decomposed into prime factors or all factors.

The factors[n] function will return the prime decomposition of n.

The allFactors[n, include1=true, includeN=true, sort=true, onlyToSqrt=false] function will return all factors of n. The optional arguments include1 and includeN indicate if the numbers 1 and n are to be included in the results. If the optional argument sort is true, the results will be sorted. If the optional argument onlyToSqrt=true, then only the factors less than or equal to the square root of the number will be produced.

The following produces all factors of n, including 1 and n:

allFactors[n]

## FunL

Function to compute set of factors:

def factors( n ) = {d | d <- 1..n if d|n}

Test:

for x <- [103, 316, 519, 639, 760]
println( 'The set of factors of ' + x + ' is ' + factors(x) )
Output:
The set of factors of 103 is {1, 103}
The set of factors of 316 is {158, 4, 79, 1, 2, 316}
The set of factors of 519 is {1, 3, 173, 519}
The set of factors of 639 is {9, 639, 71, 213, 1, 3}
The set of factors of 760 is {8, 19, 4, 40, 152, 5, 10, 76, 1, 95, 190, 760, 20, 2, 38, 380}


## FutureBasic

window 1, @"Factors of an Integer", (0,0,1000,270)

clear local mode
local fn IntegerFactors( f as long ) as CFStringRef
long        i, s, l(100), c = 0
CFStringRef factorStr = @""

for i = 1 to sqr(f)
if ( f mod i == 0 )
l(c) = i
c++
if ( f != i ^ 2 )
l(c) = ( f / i )
c++
end if
end if
next i

s = 1
while ( s = 1 )
s = 0
for i = 0 to c-1
if l(i) > l(i+1) and l(i+1) != 0
swap l(i), l(i+1)
s = 1
end if
next i
wend

for i = 0 to c - 1
if ( i < c - 1 )
factorStr = fn StringWithFormat( @"%@ %ld, ", factorStr, l(i) )
else
factorStr = fn StringWithFormat( @"%@ %ld", factorStr, l(i) )
end if
next
end fn = factorStr

print @"Factors of 25 are:"; fn IntegerFactors( 25 )
print @"Factors of 45 are:"; fn IntegerFactors( 45 )
print @"Factors of 103 are:"; fn IntegerFactors( 103 )
print @"Factors of 760 are:"; fn IntegerFactors( 760 )
print @"Factors of 12345 are:"; fn IntegerFactors( 12345 )
print @"Factors of 32766 are:"; fn IntegerFactors( 32766 )
print @"Factors of 32767 are:"; fn IntegerFactors( 32767 )
print @"Factors of 57097 are:"; fn IntegerFactors( 57097 )
print @"Factors of 12345678 are:"; fn IntegerFactors( 12345678 )
print @"Factors of 32434243 are:"; fn IntegerFactors( 32434243 )

HandleEvents

Output:

Factors of 25 are: 1, 5, 25
Factors of 45 are: 1, 3, 5, 9, 15, 45
Factors of 103 are: 1, 103
Factors of 760 are: 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
Factors of 12345 are: 1, 3, 5, 15, 823, 2469, 4115, 12345
Factors of 32766 are: 1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766
Factors of 32767 are: 1, 7, 31, 151, 217, 1057, 4681, 32767
Factors of 57097 are: 1, 57097
Factors of 12345678 are: 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 14593, 29186, 43779, 87558, 131337, 262674, 685871, 1371742, 2057613, 4115226, 6172839, 12345678
Factors of 32434243 are: 1, 307, 105649, 32434243


## GAP

# Built-in function
DivisorsInt(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]

# A possible implementation, not suitable to large n
div := n -> Filtered([1 .. n], k -> n mod k = 0);

div(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]

# Another implementation, usable for large n (if n can be factored quickly)
div2 := function(n)
local f, p;
f := Collected(FactorsInt(n));
p := List(f, v -> List([0 .. v[2]], k -> v[1]^k));
return SortedList(List(Cartesian(p), Product));
end;

div2(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]


## Go

Trial division, no prime number generator, but with some optimizations. It's good enough to factor any 64 bit integer, with large primes taking several seconds.

package main

import "fmt"

func main() {
printFactors(-1)
printFactors(0)
printFactors(1)
printFactors(2)
printFactors(3)
printFactors(53)
printFactors(45)
printFactors(64)
printFactors(600851475143)
printFactors(999999999999999989)
}

func printFactors(nr int64) {
if nr < 1 {
fmt.Println("\nFactors of", nr, "not computed")
return
}
fmt.Printf("\nFactors of %d: ", nr)
fs := make([]int64, 1)
fs[0] = 1
apf := func(p int64, e int) {
n := len(fs)
for i, pp := 0, p; i < e; i, pp = i+1, pp*p {
for j := 0; j < n; j++ {
fs = append(fs, fs[j]*pp)
}
}
}
e := 0
for ; nr & 1 == 0; e++ {
nr >>= 1
}
apf(2, e)
for d := int64(3); nr > 1; d += 2 {
if d*d > nr {
d = nr
}
for e = 0; nr%d == 0; e++ {
nr /= d
}
if e > 0 {
apf(d, e)
}
}
fmt.Println(fs)
fmt.Println("Number of factors =", len(fs))
}

Output:
Factors of -1 not computed

Factors of 0 not computed

Factors of 1: [1]
Number of factors = 1

Factors of 2: [1 2]
Number of factors = 2

Factors of 3: [1 3]
Number of factors = 2

Factors of 53: [1 53]
Number of factors = 2

Factors of 45: [1 3 9 5 15 45]
Number of factors = 6

Factors of 64: [1 2 4 8 16 32 64]
Number of factors = 7

Factors of 600851475143: [1 71 839 59569 1471 104441 1234169 87625999 6857 486847 5753023 408464633 10086647 716151937 8462696833 600851475143]
Number of factors = 16

Factors of 999999999999999989: [1 999999999999999989]
Number of factors = 2

## Gosu

var numbers = {11, 21, 32, 45, 67, 96}
numbers.each(\ number -> printFactors(number))

function printFactors(n: int) {
if (n < 1) return
var result ="${n} => " (1 .. n/2).each(\ i -> {result += n % i == 0 ? "${i} " : ""})
print("${result}${n}")
}

Output:
11 => 1 11
21 => 1 3 7 21
32 => 1 2 4 8 16 32
45 => 1 3 5 9 15 45
67 => 1 67
96 => 1 2 3 4 6 8 12 16 24 32 48 96


## Groovy

A straight brute force approach up to the square root of N:

def factorize = { long target ->

if (target == 1) return [1L]

if (target < 4) return [1L, target]

def targetSqrt = Math.sqrt(target)
def lowfactors = (2L..targetSqrt).grep { (target % it) == 0 }
if (lowfactors == []) return [1L, target]
def nhalf = lowfactors.size() - ((lowfactors[-1] == targetSqrt) ? 1 : 0)

[1] + lowfactors + (0..<nhalf).collect { target.intdiv(lowfactors[it]) }.reverse() + [target]
}


Test:

((1..30) + [333333]).each { println ([number:it, factors:factorize(it)]) }

Output:
[number:1, factors:[1]]
[number:2, factors:[1, 2]]
[number:3, factors:[1, 3]]
[number:4, factors:[1, 2, 4]]
[number:5, factors:[1, 5]]
[number:6, factors:[1, 2, 3, 6]]
[number:7, factors:[1, 7]]
[number:8, factors:[1, 2, 4, 8]]
[number:9, factors:[1, 3, 9]]
[number:10, factors:[1, 2, 5, 10]]
[number:11, factors:[1, 11]]
[number:12, factors:[1, 2, 3, 4, 6, 12]]
[number:13, factors:[1, 13]]
[number:14, factors:[1, 2, 7, 14]]
[number:15, factors:[1, 3, 5, 15]]
[number:16, factors:[1, 2, 4, 8, 16]]
[number:17, factors:[1, 17]]
[number:18, factors:[1, 2, 3, 6, 9, 18]]
[number:19, factors:[1, 19]]
[number:20, factors:[1, 2, 4, 5, 10, 20]]
[number:21, factors:[1, 3, 7, 21]]
[number:22, factors:[1, 2, 11, 22]]
[number:23, factors:[1, 23]]
[number:24, factors:[1, 2, 3, 4, 6, 8, 12, 24]]
[number:25, factors:[1, 5, 25]]
[number:26, factors:[1, 2, 13, 26]]
[number:27, factors:[1, 3, 9, 27]]
[number:28, factors:[1, 2, 4, 7, 14, 28]]
[number:29, factors:[1, 29]]
[number:30, factors:[1, 2, 3, 5, 6, 10, 15, 30]]
[number:333333, factors:[1, 3, 7, 9, 11, 13, 21, 33, 37, 39, 63, 77, 91, 99, 111, 117, 143, 231, 259, 273, 333, 407, 429, 481, 693, 777, 819, 1001, 1221, 1287, 1443, 2331, 2849, 3003, 3367, 3663, 4329, 5291, 8547, 9009, 10101, 15873, 25641, 30303, 37037, 47619, 111111, 333333]]

Using D. Amos'es Primes module for finding prime factors

import HFM.Primes (primePowerFactors)
import Data.List (product)

-- primePowerFactors :: Integer -> [(Integer,Int)]

factors = map product .
mapM (p,m)-> [p^i | i<-[0..m]]) . primePowerFactors  Returns list of factors out of order, e.g.: ~> factors 42 [1,7,3,21,2,14,6,42]  Or, prime decomposition task can be used (although, a trial division-only version will become very slow for large primes), import Data.List (group) primePowerFactors = map (\x-> (head x, length x)) . group . factorize  The above function can also be found in the package arithmoi, as Math.NumberTheory.Primes.factorise :: Integer -> [(Integer, Int)], which performs "factorisation of Integers by the elliptic curve algorithm after Montgomery" and "is best suited for numbers of up to 50-60 digits". Or, deriving cofactors from factors up to the square root: integerFactors :: Int -> [Int] integerFactors n | 1 > n = [] | otherwise = lows <> (quot n <> part n (reverse lows)) where part n | n == square = tail | otherwise = id (square, lows) = (,) . (^ 2) <*> (filter ((0 ==) . rem n) . enumFromTo 1)  floor (sqrt  fromIntegral n) main :: IO () main = print  integerFactors 600  Output: [1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600] ### List comprehension Naive, functional, no import, in increasing order: factorsNaive n = [ i | i <- [1 .. n] , mod n i == 0 ]  ~> factorsNaive 25 [1,5,25]  Factor, cofactor. Get the list of factor–cofactor pairs sorted, for a quadratic speedup: import Data.List (sort) factorsCo n = sort [ i | i <- [1 .. floor (sqrt (fromIntegral n))] , (d, 0) <- [divMod n i] , i <- i : [ d | d > i ] ]  A version of the above without the need for sorting, making it to be online (i.e. productive immediately, which can be seen in GHCi); factors in increasing order: factorsO n = ds ++ [ r | (d, 0) <- [divMod n r] , r <- r : [ d | d > r ] ] ++ reverse (map (n div) ds) where r = floor (sqrt (fromIntegral n)) ds = [ i | i <- [1 .. r - 1] , mod n i == 0 ]  Testing: *Main> :set +s ~> factorsO 120 [1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120] (0.00 secs, 0 bytes) ~> factorsO 12041111117 [1,7,41,287,541,3787,22181,77551,155267,542857,3179591,22257137,41955091,2936856 37,1720158731,12041111117] (0.09 secs, 50758224 bytes)  ## HicEst  DLG(NameEdit=N, TItle='Enter an integer') DO i = 1, N^0.5 IF( MOD(N,i) == 0) WRITE() i, N/i ENDDO END ## Icon and Unicon procedure main(arglist) numbers := arglist ||| [ 32767, 45, 53, 64, 100] # combine command line provided and default set of values every writes(lf,"factors of ",i := !numbers,"=") & writes(divisors(i)," ") do lf := "\n" end link factors  Output: factors of 32767=1 7 31 151 217 1057 4681 32767 factors of 45=1 3 5 9 15 45 factors of 53=1 53 factors of 64=1 2 4 8 16 32 64 factors of 100=1 2 4 5 10 20 25 50 100 divisors ## J The "brute force" approach is the most concise: foi=: [: I. 0 = (|~ i.@>:)  Example use:  foi 40 1 2 4 5 8 10 20 40  Basically we test every non-negative integer up through the number itself to see if it divides evenly. However, this becomes very slow for large numbers. So other approaches can be worthwhile. J has a primitive, q: which returns its argument's prime factors. q: 40 2 2 2 5  Alternatively, q: can produce provide a table of the exponents of the unique relevant prime factors  __ q: 420 2 3 5 7 2 1 1 1  With this, we can form lists of each of the potential relevant powers of each of these prime factors  (^ i.@>:)&.>/ __ q: 420 ┌─────┬───┬───┬───┐ │1 2 4│1 3│1 5│1 7│ └─────┴───┴───┴───┘  From here, it's a simple matter (*/&>@{ or, find all possible combinations of one item from each list ({ without a left argument) then unpack each list and multiply its elements) to compute all possible factors of the original number factrs=: */&>@{@((^ i.@>:)&.>/)@q:~&__ factrs 40 1 5 2 10 4 20 8 40  However, a data structure which is organized around the prime decomposition of the argument can be hard to read. So, for reader convenience, we should probably arrange them in a monotonically increasing list:  factors=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__ factors 420 1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 140 210 420  A less efficient, but concise variation on this theme:  ~.,*/&> { 1 ,&.> q: 40 1 5 2 10 4 20 8 40  This computes 2^n intermediate values where n is the number of prime factors of the original number. That said, note that we get a representation issue when dealing with large numbers:  factors 568474220 1 2 4 5 10 17 20 34 68 85 170 340 1.67198e6 3.34397e6 6.68793e6 8.35992e6 1.67198e7 2.84237e7 3.34397e7 5.68474e7 1.13695e8 1.42119e8 2.84237e8 5.68474e8  One approach here (if we don't want to explicitly format the result) is to use an arbitrary precision (aka "extended") argument. This propagates through into the result:  factors 568474220x 1 2 4 5 10 17 20 34 68 85 170 340 1671983 3343966 6687932 8359915 16719830 28423711 33439660 56847422 113694844 142118555 284237110 568474220  Another less efficient approach, in which remainders are examined up to the square root, larger factors obtained as fractions, and the combined list nubbed and sorted might be: factorsOfNumber=: monad define Y=. y"_ /:~ ~. ( , Y%]) ( #~ 0=]|Y) 1+i.>.%:y ) factorsOfNumber 40 1 2 4 5 8 10 20 40  Another approach: odometer =: #: i.@(*/) factors=: (*/@:^"1 odometer@:>:)/@q:~&__  ## Java Works with: Java version 5+ public static TreeSet<Long> factors(long n) { TreeSet<Long> factors = new TreeSet<Long>(); factors.add(n); factors.add(1L); for(long test = n - 1; test >= Math.sqrt(n); test--) if(n % test == 0) { factors.add(test); factors.add(n / test); } return factors; }  ## JavaScript ### Imperative function factors(num) { var n_factors = [], i; for (i = 1; i <= Math.floor(Math.sqrt(num)); i += 1) if (num % i === 0) { n_factors.push(i); if (num / i !== i) n_factors.push(num / i); } n_factors.sort(function(a, b){return a - b;}); // numeric sort return n_factors; } factors(45); // [1,3,5,9,15,45] factors(53); // [1,53] factors(64); // [1,2,4,8,16,32,64]  ### Functional #### ES5 Translating the naive list comprehension example from Haskell, using a list monad for the comprehension // Monadic bind (chain) for lists function chain(xs, f) { return [].concat.apply([], xs.map(f)); } // [m..n] function range(m, n) { return Array.apply(null, Array(n - m + 1)).map(function (x, i) { return m + i; }); } function factors_naive(n) { return chain( range(1, n), function (x) { // monadic chain/bind return n % x ? [] : [x]; // monadic fail or inject/return }); } factors_naive(6)  Output: [1, 2, 3, 6]  Translating the Haskell (lows and highs) example console.log( (function (lstTest) { // INTEGER FACTORS function integerFactors(n) { var rRoot = Math.sqrt(n), intRoot = Math.floor(rRoot), lows = range(1, intRoot).filter(function (x) { return (n % x) === 0; }); // for perfect squares, we can drop the head of the 'highs' list return lows.concat(lows.map(function (x) { return n / x; }).reverse().slice((rRoot === intRoot) | 0)); } // [m .. n] function range(m, n) { return Array.apply(null, Array(n - m + 1)).map(function (x, i) { return m + i; }); } /*************************** TESTING *****************************/ // TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS function alignedTable(lstRows, lngPad, fnAligned) { var lstColWidths = range(0, lstRows.reduce(function (a, x) { return x.length > a ? x.length : a; }, 0) - 1).map(function (iCol) { return lstRows.reduce(function (a, lst) { var w = lst[iCol] ? lst[iCol].toString().length : 0; return (w > a) ? w : a; }, 0); }); return lstRows.map(function (lstRow) { return lstRow.map(function (v, i) { return fnAligned(v, lstColWidths[i] + lngPad); }).join('') }).join('\n'); } function alignRight(n, lngWidth) { var s = n.toString(); return Array(lngWidth - s.length + 1).join(' ') + s; } // TEST return '\nintegerFactors(n)\n\n' + alignedTable( lstTest.map(integerFactors).map(function (x, i) { return [lstTest[i], '-->'].concat(x); }), 2, alignRight ) + '\n'; })([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767]) );  Output: integerFactors(n) 25 --> 1 5 25 45 --> 1 3 5 9 15 45 53 --> 1 53 64 --> 1 2 4 8 16 32 64 100 --> 1 2 4 5 10 20 25 50 100 102 --> 1 2 3 6 17 34 51 102 120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 12345 --> 1 3 5 15 823 2469 4115 12345 32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766 32767 --> 1 7 31 151 217 1057 4681 32767  #### ES6 (function (lstTest) { 'use strict'; // INTEGER FACTORS // integerFactors :: Int -> [Int] let integerFactors = (n) => { let rRoot = Math.sqrt(n), intRoot = Math.floor(rRoot), lows = range(1, intRoot) .filter(x => (n % x) === 0); // for perfect squares, we can drop // the head of the 'highs' list return lows.concat(lows .map(x => n / x) .reverse() .slice((rRoot === intRoot) | 0) ); }, // range :: Int -> Int -> [Int] range = (m, n) => Array.from({ length: (n - m) + 1 }, (_, i) => m + i); /*************************** TESTING *****************************/ // TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS let alignedTable = (lstRows, lngPad, fnAligned) => { var lstColWidths = range( 0, lstRows .reduce( (a, x) => (x.length > a ? x.length : a), 0 ) - 1 ) .map((iCol) => lstRows .reduce((a, lst) => { let w = lst[iCol] ? lst[iCol].toString() .length : 0; return (w > a) ? w : a; }, 0)); return lstRows.map((lstRow) => lstRow.map((v, i) => fnAligned( v, lstColWidths[i] + lngPad )) .join('') ) .join('\n'); }, alignRight = (n, lngWidth) => { let s = n.toString(); return Array(lngWidth - s.length + 1) .join(' ') + s; }; // TEST return '\nintegerFactors(n)\n\n' + alignedTable(lstTest .map(integerFactors) .map( (x, i) => [lstTest[i], '-->'].concat(x) ), 2, alignRight ) + '\n'; })([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767]);  Output: integerFactors(n) 25 --> 1 5 25 45 --> 1 3 5 9 15 45 53 --> 1 53 64 --> 1 2 4 8 16 32 64 100 --> 1 2 4 5 10 20 25 50 100 102 --> 1 2 3 6 17 34 51 102 120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 12345 --> 1 3 5 15 823 2469 4115 12345 32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766 32767 --> 1 7 31 151 217 1057 4681 32767  ## jq Works with: jq version 1.4 # This implementation uses "sort" for tidiness def factors: . as num | reduce range(1; 1 + sqrt|floor) as i ([]; if (num % i) == 0 then (num / i) as r | if i == r then . + [i] else . + [i, r] end else . end ) | sort; def task: (45, 53, 64) | "\(.): \(factors)" ; task Output:  jq -n -M -r -c -f factors.jq 45: [1,3,5,9,15,45] 53: [1,53] 64: [1,2,4,8,16,32,64]  ## Julia using Primes function factors(n) f = [one(n)] for (p,e) in factor(n) f = reduce(vcat, [f*p^j for j in 1:e], init=f) end return length(f) == 1 ? [one(n), n] : sort!(f) end const examples = [28, 45, 53, 64, 6435789435768] for n in examples @time println("The factors of n are: (factors(n))") end  Output: The factors of 28 are: [1, 2, 4, 7, 14, 28] 0.330684 seconds (784.75 k allocations: 39.104 MiB, 3.17% gc time) The factors of 45 are: [1, 3, 5, 9, 15, 45] 0.000117 seconds (56 allocations: 2.672 KiB) The factors of 53 are: [1, 53] 0.000102 seconds (35 allocations: 1.516 KiB) The factors of 64 are: [1, 2, 4, 8, 16, 32, 64] 0.000093 seconds (56 allocations: 3.172 KiB) The factors of 6435789435768 are: [1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 191, 231, 264, 308, 382, 462, 573, 616, 764, 924, 1146, 1337, 1528, 1848, 2101, 2292, 2674, 4011, 4202, 4584, 5348, 6303, 8022, 8404, 10696, 12606, 14707, 16044, 16808, 25212, 29414, 32088, 44121, 50424, 58828, 88242, 117656, 176484, 352968, 18233351, 36466702, 54700053, 72933404, 109400106, 127633457, 145866808, 200566861, 218800212, 255266914, 382900371, 401133722, 437600424, 510533828, 601700583, 765800742, 802267444, 1021067656, 1203401166, 1403968027, 1531601484, 1604534888, 2406802332, 2807936054, 3063202968, 3482570041, 4211904081, 4813604664, 5615872108, 6965140082, 8423808162, 10447710123, 11231744216, 13930280164, 16847616324, 20895420246, 24377990287, 27860560328, 33695232648, 38308270451, 41790840492, 48755980574, 73133970861, 76616540902, 83581680984, 97511961148, 114924811353, 146267941722, 153233081804, 195023922296, 229849622706, 268157893157, 292535883444, 306466163608, 459699245412, 536315786314, 585071766888, 804473679471, 919398490824, 1072631572628, 1608947358942, 2145263145256, 3217894717884, 6435789435768] 0.000249 seconds (451 allocations: 24.813 KiB)  ## K  f:{i:{y[&x=y*x div y]}[x;1+!_sqrt x];?i,x div|i} equivalent to: q)f:{i:{y where x=y*x div y}[x ; 1+ til floor sqrt x]; distinct i,x div reverse i} f 120 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 f 1024 1 2 4 8 16 32 64 128 256 512 1024 f 600851475143 1 71 839 1471 6857 59569 104441 486847 1234169 5753023 10086647 87625999 408464633 716151937 8462696833 600851475143 #f 3491888400 / has 1920 factors 1920 / Number of factors for 3491888400 .. 3491888409 #:'f' 3491888400+!10 1920 16 4 4 12 16 32 16 8 24 ## Kotlin fun printFactors(n: Int) { if (n < 1) return print("n => ") (1..n / 2) .filter { n % it == 0 } .forEach { print("it ") } println(n) } fun main(args: Array<String>) { val numbers = intArrayOf(11, 21, 32, 45, 67, 96) for (number in numbers) printFactors(number) }  Output: 11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 16 32 45 => 1 3 5 9 15 45 67 => 1 67 96 => 1 2 3 4 6 8 12 16 24 32 48 96  ## Lambdatalk {def factors {def factors.r {lambda {:num :i :N} {if {> :i :N} then else {if {= {% :num :i} 0} then :i {if {not {= {/ :num :i} :i}} then {/ :num :i} else} else} {factors.r :num {+ :i 1} :N} }}} {lambda {:n} {S.sort < {factors.r :n 1 {sqrt :n}}}}} -> factors {factors 45} -> 1 3 5 9 15 45 {factors 53} -> 1 53 {factors 64} -> 1 2 4 8 16 32 64  ## LFE ### Using List Comprehensions This following function is elegant looking and concise. However, it will not handle large numbers well: it will consume a great deal of memory (on one large number, the function consumed 4.3GB of memory on my desktop machine): (defun factors (n) (list-comp ((<- i (when (== 0 (rem n i))) (lists:seq 1 (trunc (/ n 2))))) i))  ### Non-Stack-Consuming This version will not consume the stack (this function only used 18MB of memory on my machine with a ridiculously large number): (defun factors (n) "Tail-recursive prime factors function." (factors n 2 '())) (defun factors ((1 _ acc) (++ acc '(1))) ((n _ acc) (when (=< n 0)) #(error undefined)) ((n k acc) (when (== 0 (rem n k))) (factors (div n k) k (cons k acc))) ((n k acc) (factors n (+ k 1) acc)))  Output: > (factors 10677106534462215678539721403561279) (104729 104729 104729 98731 98731 32579 29269 1)  ## Liberty BASIC num = 10677106534462215678539721403561279 maxnFactors = 1000 dim primeFactors(maxnFactors), nPrimeFactors(maxnFactors) global nDifferentPrimeNumbersFound, nFactors, iFactor print "Start finding all factors of ";num; ":" nDifferentPrimeNumbersFound=0 dummy = factorize(num,2) nFactors = showPrimeFactors(num) dim factors(nFactors) dummy = generateFactors(1,1) sort factors(), 0, nFactors-1 for i=1 to nFactors print i;" ";factors(i-1) next i print "done" wait function factorize(iNum,offset) factorFound=0 i = offset do if (iNum MOD i)=0 _ then if primeFactors(nDifferentPrimeNumbersFound) = i _ then nPrimeFactors(nDifferentPrimeNumbersFound) = nPrimeFactors(nDifferentPrimeNumbersFound) + 1 else nDifferentPrimeNumbersFound = nDifferentPrimeNumbersFound + 1 primeFactors(nDifferentPrimeNumbersFound) = i nPrimeFactors(nDifferentPrimeNumbersFound) = 1 end if if iNum/i<>1 then dummy = factorize(iNum/i,i) factorFound=1 end if i=i+1 loop while factorFound=0 and i<=sqr(iNum) if factorFound=0 _ then nDifferentPrimeNumbersFound = nDifferentPrimeNumbersFound + 1 primeFactors(nDifferentPrimeNumbersFound) = iNum nPrimeFactors(nDifferentPrimeNumbersFound) = 1 end if end function function showPrimeFactors(iNum) showPrimeFactors=1 print iNum;" = "; for i=1 to nDifferentPrimeNumbersFound print primeFactors(i);"^";nPrimeFactors(i); if i<nDifferentPrimeNumbersFound then print " * "; else print "" showPrimeFactors = showPrimeFactors*(nPrimeFactors(i)+1) next i end function function generateFactors(product,pIndex) if pIndex>nDifferentPrimeNumbersFound _ then factors(iFactor) = product iFactor=iFactor+1 else for i=0 to nPrimeFactors(pIndex) dummy = generateFactors(product*primeFactors(pIndex)^i,pIndex+1) next i end if end function Output: Start finding all factors of 10677106534462215678539721403561279: 10677106534462215678539721403561279 = 29269^1 * 32579^1 * 98731^2 * 104729^3 1 1 2 29269 3 32579 4 98731 5 104729 6 953554751 7 2889757639 8 3065313101 9 3216557249 10 3411966091 11 9747810361 12 10339998899 13 10968163441 14 94145414120981 15 99864835517479 16 285308661456109 17 302641427774831 18 317573913751019 19 321027175754629 20 336866824130521 21 357331796744339 22 1020878431297169 23 1082897744693371 24 1148684789012489 25 9295070881578575111 26 9859755075476219149 27 10458744358910058191 28 29880090805636839461 29 31695334089430275799 30 33259198413230468851 31 33620855089606540541 32 35279725624365333809 33 37423001741237879131 34 106915577231321212201 35 113410797903992051459 36 973463478356842592799919 37 1032602289299548955255621 38 1095333837964291484285239 39 3129312029983540559911069 40 3319420643851943354153471 41 3483202590619213772296379 42 3694810384914157044482761 43 11197161487859039232598529 44 101949856624833767901342716951 45 108143405156052462534965931709 46 327729719588146219298926345301 47 364792324112959639158827476291 48 10677106534462215678539721403561279 done ### A Simpler Approach This is a somewhat simpler approach for finding the factors of smaller numbers (less than one million). print "ROSETTA CODE - Factors of an integer" 'A simpler approach for smaller numbers [Start] print input "Enter an integer (< 1,000,000): "; n n=abs(int(n)): if n=0 then goto [Quit] if n>999999 then goto [Start] FactorCount=FactorCount(n) select case FactorCount case 1: print "The factor of 1 is: 1" case else print "The "; FactorCount; " factors of "; n; " are: "; for x=1 to FactorCount print " "; Factor(x); next x if FactorCount=2 then print " (Prime)" else print end select goto [Start] [Quit] print "Program complete." end function FactorCount(n) dim Factor(100) for y=1 to n if y>sqr(n) and FactorCount=1 then 'If no second factor is found by the square root of n, then n is prime. FactorCount=2: Factor(FactorCount)=n: exit function end if if (n mod y)=0 then FactorCount=FactorCount+1 Factor(FactorCount)=y end if next y end function Output: ROSETTA CODE - Factors of an integer Enter an integer (< 1,000,000): 1 The factor of 1 is: 1 Enter an integer (< 1,000,000): 2 The 2 factors of 2 are: 1 2 (Prime) Enter an integer (< 1,000,000): 4 The 3 factors of 4 are: 1 2 4 Enter an integer (< 1,000,000): 6 The 4 factors of 6 are: 1 2 3 6 Enter an integer (< 1,000,000): 999999 The 64 factors of 999999 are: 1 3 7 9 11 13 21 27 33 37 39 63 77 91 99 111 117 143 189 231 259 273 297 333 351 407 429 481 693 777 819 999 1001 1221 1287 1443 2079 2331 2457 2849 3003 3367 3663 3861 4329 5291 6993 8547 9009 10101 10989 129 87 15873 25641 27027 30303 37037 47619 76923 90909 111111 142857 333333 999999 Enter an integer (< 1,000,000): Program complete.  ## Lingo on factors(n) res = [1] repeat with i = 2 to n/2 if n mod i = 0 then res.add(i) end repeat res.add(n) return res end put factors(45) -- [1, 3, 5, 9, 15, 45] put factors(53) -- [1, 53] put factors(64) -- [1, 2, 4, 8, 16, 32, 64] ## Logo to factors :n output filter [equal? 0 modulo :n ?] iseq 1 :n end show factors 28 ; [1 2 4 7 14 28] ## Lua function Factors( n ) local f = {} for i = 1, n/2 do if n % i == 0 then f[#f+1] = i end end f[#f+1] = n return f end  ## M2000 Interpreter \\ Factors of an integer \\ For act as BASIC's FOR (if N<1 no loop start) FORM 60,40 SET SWITCHES "+FOR" MODULE LikeBasic { 10 INPUT N% 20 FOR I%=1 TO N% 30 IF N%/I%=INT(N%/I%) THEN PRINT I%, 40 NEXT I% 50 PRINT } CALL LikeBasic SET SWITCHES "-FOR" MODULE LikeM2000 { DEF DECIMAL N%, I% INPUT N% IF N%<1 THEN EXIT FOR I%=1 TO N% { IF N% MOD I%=0 THEN PRINT I%, } PRINT } CALL LikeM2000 ## Maple numtheory:-divisors(n); ## Mathematica / Wolfram Language Factorize[n_Integer] := Divisors[n]  ## MATLAB / Octave  function fact(n); f = factor(n); % prime decomposition K = dec2bin(0:2^length(f)-1)-'0'; % generate all possible permutations F = ones(1,2^length(f)); for k = 1:size(K) F(k) = prod(f(~K(k,:))); % and compute products end; F = unique(F); % eliminate duplicates printf('There are %i factors for %i.\n',length(F),n); disp(F); end;  Output: >> fact(12) There are 6 factors for 12. 1 2 3 4 6 12 >> fact(28) There are 6 factors for 28. 1 2 4 7 14 28 >> fact(64) There are 7 factors for 64. 1 2 4 8 16 32 64 >>fact(53) There are 2 factors for 53. 1 53  ## Maxima The builtin divisors function does this. (%i96) divisors(100); (%o96) {1,2,4,5,10,20,25,50,100}  Such a function could be implemented like so: divisors2(n) := map( lambda([l], lreduce("*", l)), apply( cartesian_product, map( lambda([fac], setify(makelist(fac[1]^i, i, 0, fac[2]))), ifactors(n))));  ## MAXScript fn factors n = ( return (for i = 1 to n+1 where mod n i == 0 collect i) ) Output: factors 3 #(1, 3) factors 7 #(1, 7) factors 14 #(1, 2, 7, 14) factors 60 #(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) factors 54 #(1, 2, 3, 6, 9, 18, 27, 54) ## Mercury Mercury is both a logic language and a functional language. As such there are two possible interfaces for calculating the factors of an integer. This code shows both styles of implementation. Note that much of the code here is ceremony put in place to have this be something which can actually compile. The actual factoring is contained in the predicate factor/2 and in the function factor/1. The function form is implemented in terms of the predicate form rather than duplicating all of the predicate code. The predicates main/2 and factor/2 are shown with the combined type and mode statement (e.g. int::in) as is the usual case for simple predicates with only one mode. This makes the code more immediately understandable. The predicate factor/5, however, has its mode broken out onto a separate line both to show Mercury's mode statement (useful for predicates which can have varying instantiation of parameters) and to stop the code from extending too far to the right. Finally the function factor/1 has its mode statements removed (shown underneath in a comment for illustration purposes) because good coding style (and the default of the compiler!) has all parameters "in"-moded and the return value "out"-moded. This implementation of factoring works as follows: 1. The input number itself and 1 are both considered factors. 2. The numbers between 2 and the square root of the input number are checked for even division. 3. If the incremental number divides evenly into the input number, both the incremental number and the quotient are added to the list of factors. This implementation makes use of Mercury's "state variable notation" to keep a pair of variables for accumulation, thus allowing the implementation to be tail recursive. !Accumulator is syntax sugar for a *pair* of variables. One of them is an "in"-moded variable and the other is an "out"-moded variable. !:Accumulator is the "out" portion and !.Accumulator is the "in" portion in the ensuing code. Using the state variable notation avoids having to keep track of strings of variables unified in the code named things like Acc0, Acc1, Acc2, Acc3, etc. ### fac.m :- module fac. :- interface. :- import_module io. :- pred main(io::di, io::uo) is det. :- implementation. :- import_module float, int, list, math, string. main(!IO) :- io.command_line_arguments(Args, !IO), list.filter_map(string.to_int, Args, CleanArgs), list.foldl((pred(Arg::in, !.IO::di, !:IO::uo) is det :- factor(Arg, X), io.format("factor(%d, [", [i(Arg)], !IO), io.write_list(X, ",", io.write_int, !IO), io.write_string("])\n", !IO) ), CleanArgs, !IO). :- pred factor(int::in, list(int)::out) is det. factor(N, Factors) :- Limit = float.truncate_to_int(math.sqrt(float(N))), factor(N, 2, Limit, [], Unsorted), list.sort_and_remove_dups([1, N | Unsorted], Factors). :- pred factor(int, int, int, list(int), list(int)). :- mode factor(in, in, in, in, out) is det. factor(N, X, Limit, !Accumulator) :- ( if X > Limit then true else ( if 0 = N mod X then !:Accumulator = [X, N / X | !.Accumulator] else true ), factor(N, X + 1, Limit, !Accumulator) ). :- func factor(int) = list(int). %:- mode factor(in) = out is det. factor(N) = Factors :- factor(N, Factors). :- end_module fac. ### Use and output Use of the code looks like this:  mmc fac.m && ./fac 100 999 12345678 booger factor(100, [1,2,4,5,10,20,25,50,100]) factor(999, [1,3,9,27,37,111,333,999]) factor(12345678, [1,2,3,6,9,18,47,94,141,282,423,846,14593,29186,43779,87558,131337,262674,685871,1371742,2057613,4115226,6172839,12345678]) ## min Works with: min version 0.19.6 (mod 0 ==) :divisor? (() 0 shorten) :new (new (over swons 'pred dip) pick times nip) :iota ( :n n sqrt int iota ; Only consider numbers up to sqrt(n). (n swap divisor?) filter =f1 f1 (n swap div) map reverse =f2 ; "Mirror" the list of divisors at sqrt(n). (f1 last f2 first ==) (f2 rest #f2) when ; Handle perfect squares. f1 f2 concat ) :factors 24 factors puts! 9 factors puts! 11 factors puts! ## MiniScript factors = function(n) result = [1] for i in range(2, n) if n % i == 0 then result.push i end for return result end function while true n = val(input("Number to factor (0 to quit)? ")) if n <= 0 then break print factors(n) end while  Output: Number to factor (0 to quit)? 42 [1, 2, 3, 6, 7, 14, 21, 42] Number to factor (0 to quit)? 101 [1, 101] Number to factor (0 to quit)? 360 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360] Number to factor (0 to quit)? 0 ## МК-61/52 П9 1 П6 КИП6 ИП9 ИП6 / П8 ^ [x] x#0 21 - x=0 03 ИП6 С/П ИП8 П9 БП 04 1 С/П БП 21  ## MUMPS factors(num) New fctr,list,sep,sqrt If num<1 Quit "Too small a number" If num["." Quit "Not an integer" Set sqrt=num**0.5\1 For fctr=1:1:sqrt Set:num/fctr'["." list(fctr)=1,list(num/fctr)=1 Set (list,fctr)="",sep="[" For Set fctr=Order(list(fctr)) Quit:fctr="" Set list=list_sep_fctr,sep="," Quit list_"]" w factors(45) ; [1,3,5,9,15,45] w factors(53) ; [1,53] w factors(64) ; [1,2,4,8,16,32,64] ## Nanoquery n = int(input()) for i in range(1, n / 2) if (n % i = 0) print i + " " end end println n ## NetRexx Translation of: REXX /* NetRexx *********************************************************** * 21.04.2013 Walter Pachl * 21.04.2013 add method main to accept argument(s) *********************************************************************/ options replace format comments java crossref symbols nobinary class divl method main(argwords=String[]) static arg=Rexx(argwords) Parse arg a b Say a b If a='' Then Do help='java divl low [high] shows' help=help||' divisors of all numbers between low and high' Say help Return End If b='' Then b=a loop x=a To b say x '->' divs(x) End method divs(x) public static returns Rexx if x==1 then return 1 /*handle special case of 1 */ lo=1 hi=x odd=x//2 /* 1 if x is odd */ loop j=2+odd By 1+odd While j*j<x /*divide by numbers<sqrt(x) */ if x//j==0 then Do /*Divisible? Add two divisors:*/ lo=lo j /* list low divisors */ hi=x%j hi /* list high divisors */ End End If j*j=x Then /*for a square number as input */ lo=lo j /* add its square root */ return lo hi /* return both lists */  Output: java divl 1 10 1 -> 1 2 -> 1 2 3 -> 1 3 4 -> 1 2 4 5 -> 1 5 6 -> 1 2 3 6 7 -> 1 7 8 -> 1 2 4 8 9 -> 1 3 9 10 -> 1 2 5 10 ## Nim import intsets, math, algorithm proc factors(n: int): seq[int] = var fs: IntSet for x in 1 .. int(sqrt(float(n))): if n mod x == 0: fs.incl(x) fs.incl(n div x) for x in fs: result.add(x) result.sort() echo factors(45)  ## Niue [ 'n ; [ negative-or-zero [ , ] if [ n not-factor [ , ] when ] else ] n times n ] 'factors ; [ dup 0 <= ] 'negative-or-zero ; [ swap dup rot swap mod 0 = not ] 'not-factor ; ( tests ) 100 factors .s .clr ( => 1 2 4 5 10 20 25 50 100 ) newline 53 factors .s .clr ( => 1 53 ) newline 64 factors .s .clr ( => 1 2 4 8 16 32 64 ) newline 12 factors .s .clr ( => 1 2 3 4 6 12 ) ## Oberon-2 Oxford Oberon-2 MODULE Factors; IMPORT Out,SYSTEM; TYPE LIPool = POINTER TO ARRAY OF LONGINT; LIVector= POINTER TO LIVectorDesc; LIVectorDesc = RECORD cap: INTEGER; len: INTEGER; LIPool: LIPool; END; PROCEDURE New(cap: INTEGER): LIVector; VAR v: LIVector; BEGIN NEW(v); v.cap := cap; v.len := 0; NEW(v.LIPool,cap); RETURN v END New; PROCEDURE (v: LIVector) Add(x: LONGINT); VAR newLIPool: LIPool; BEGIN IF v.len = LEN(v.LIPool^) THEN (* run out of space *) v.cap := v.cap + (v.cap DIV 2); NEW(newLIPool,v.cap); SYSTEM.MOVE(SYSTEM.ADR(v.LIPool^),SYSTEM.ADR(newLIPool^),v.cap * SIZE(LONGINT)); v.LIPool := newLIPool END; v.LIPool[v.len] := x; INC(v.len) END Add; PROCEDURE (v: LIVector) At(idx: INTEGER): LONGINT; BEGIN RETURN v.LIPool[idx]; END At; PROCEDURE Factors(n:LONGINT): LIVector; VAR j: LONGINT; v: LIVector; BEGIN v := New(16); FOR j := 1 TO n DO IF (n MOD j) = 0 THEN v.Add(j) END; END; RETURN v END Factors; VAR v: LIVector; j: INTEGER; BEGIN v := Factors(123); FOR j := 0 TO v.len - 1 DO Out.LongInt(v.At(j),4);Out.Ln END; Out.Int(v.len,6);Out.String(" factors");Out.Ln END Factors.  Output:  1 3 41 123 4 factors  ## Objeck use IO; use Structure; bundle Default { class Basic { function : native : GenerateFactors(n : Int) ~ IntVector { factors := IntVector->New(); factors-> AddBack(1); factors->AddBack(n); for(i := 2; i * i <= n; i += 1;) { if(n % i = 0) { factors->AddBack(i); if(i * i <> n) { factors->AddBack(n / i); }; }; }; factors->Sort(); return factors; } function : Main(args : String[]) ~ Nil { numbers := [3135, 45, 60, 81]; for(i := 0; i < numbers->Size(); i += 1;) { factors := GenerateFactors(numbers[i]); Console->GetInstance()->Print("Factors of ")->Print(numbers[i])->PrintLine(" are:"); each(i : factors) { Console->GetInstance()->Print(factors->Get(i))->Print(", "); }; "\n\n"->Print(); }; } } } ## OCaml let rec range = function 0 -> [] | n -> range(n-1) @ [n] let factors n = List.filter (fun v -> (n mod v) = 0) (range n)  ## Oforth Integer method: factors self seq filter(#[ self isMultiple ]) ; 120 factors println Output: [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]  ## Oz declare fun {Factors N} Sqr = {Float.toInt {Sqrt {Int.toFloat N}}} Fs = for X in 1..Sqr append:App do if N mod X == 0 then CoFactor = N div X in if CoFactor == X then %% avoid duplicate factor {App [X]} %% when N is a square number else {App [X CoFactor]} end end end in {Sort Fs Value.'<'} end in {Show {Factors 53}} ## Panda Panda has a factor function already, it's defined as: fun factor(n) type integer->integer f where n.mod(1..n=>f)==0 45.factor ## PARI/GP divisors(n) ## Pascal Translation of: Fortran Works with: Free Pascal version 2.6.2 program Factors; var i, number: integer; begin write('Enter a number between 1 and 2147483647: '); readln(number); for i := 1 to round(sqrt(number)) - 1 do if number mod i = 0 then write (i, ' ', number div i, ' '); // Check to see if number is a square i := round(sqrt(number)); if i*i = number then write(i) else if number mod i = 0 then write(i, number/i); writeln; end.  Output: Enter a number between 1 and 2147483647: 49 1 49 7 Enter a number between 1 and 2147483647: 353435 1 25755 3 8585 5 5151 15 1717 17 1515 51 505 85 303 101 255  ### using Prime decomposition Works with: Free Pascal like [C Prime_factoring]. Insertion sort was much faster, because mostly not so many factors need to be sorted. "runtime overhead" +25% instead +100% for quicksort against no sort. Especially fast for consecutive integers. program FacOfInt; // gets factors of consecutive integers fast // limited to 1.2e11 {IFDEF FPC} {MODE DELPHI} {OPTIMIZATION ON,ALL} {COPERATORS ON} {ELSE} {APPTYPE CONSOLE} {ENDIF} uses sysutils {IFDEF WINDOWS},Windows{ENDIF} ; //###################################################################### //prime decomposition const //HCN(86) > 1.2E11 = 128,501,493,120 count of divs = 4096 7 3 1 1 1 1 1 1 1 HCN_DivCnt = 4096; type tItem = Uint64; tDivisors = array [0..HCN_DivCnt] of tItem; tpDivisor = pUint64; const //used odd size for test only SizePrDeFe = 32768;//*72 <= 64kb level I or 2 Mb ~ level 2 cache type tdigits = array [0..31] of Uint32; //the first number with 11 different prime factors = //2*3*5*7*11*13*17*19*23*29*31 = 2E11 //56 byte tprimeFac = packed record pfSumOfDivs, pfRemain : Uint64; pfDivCnt : Uint32; pfMaxIdx : Uint32; pfpotPrimIdx : array[0..9] of word; pfpotMax : array[0..11] of byte; end; tpPrimeFac = ^tprimeFac; tPrimeDecompField = array[0..SizePrDeFe-1] of tprimeFac; tPrimes = array[0..65535] of Uint32; var {ALIGN 8} SmallPrimes: tPrimes; {ALIGN 32} PrimeDecompField :tPrimeDecompField; pdfIDX,pdfOfs: NativeInt; procedure InitSmallPrimes; //get primes. #0..65535.Sieving only odd numbers const MAXLIMIT = (821641-1) shr 1; var pr : array[0..MAXLIMIT] of byte; p,j,d,flipflop :NativeUInt; Begin SmallPrimes[0] := 2; fillchar(pr[0],SizeOf(pr),#0); p := 0; repeat repeat p +=1 until pr[p]= 0; j := (p+1)*p*2; if j>MAXLIMIT then BREAK; d := 2*p+1; repeat pr[j] := 1; j += d; until j>MAXLIMIT; until false; SmallPrimes[1] := 3; SmallPrimes[2] := 5; j := 3; d := 7; flipflop := (2+1)-1;//7+2*2,11+2*1,13,17,19,23 p := 3; repeat if pr[p] = 0 then begin SmallPrimes[j] := d; inc(j); end; d += 2*flipflop; p+=flipflop; flipflop := 3-flipflop; until (p > MAXLIMIT) OR (j>High(SmallPrimes)); end; function OutPots(pD:tpPrimeFac;n:NativeInt):Ansistring; var s: String[31]; chk,p,i: NativeInt; Begin str(n,s); result := s+' :'; with pd^ do begin str(pfDivCnt:3,s); result += s+' : '; chk := 1; For n := 0 to pfMaxIdx-1 do Begin if n>0 then result += '*'; p := SmallPrimes[pfpotPrimIdx[n]]; chk *= p; str(p,s); result += s; i := pfpotMax[n]; if i >1 then Begin str(pfpotMax[n],s); result += '^'+s; repeat chk *= p; dec(i); until i <= 1; end; end; p := pfRemain; If p >1 then Begin str(p,s); chk *= p; result += '*'+s; end; str(chk,s); result += '_chk_'+s+'<'; str(pfSumOfDivs,s); result += '_SoD_'+s+'<'; end; end; function smplPrimeDecomp(n:Uint64):tprimeFac; var pr,i,pot,fac,q :NativeUInt; Begin with result do Begin pfDivCnt := 1; pfSumOfDivs := 1; pfRemain := n; pfMaxIdx := 0; pfpotPrimIdx[0] := 1; pfpotMax[0] := 0; i := 0; while i < High(SmallPrimes) do begin pr := SmallPrimes[i]; q := n DIV pr; //if n < pr*pr if pr > q then BREAK; if n = pr*q then Begin pfpotPrimIdx[pfMaxIdx] := i; pot := 0; fac := pr; repeat n := q; q := n div pr; pot+=1; fac *= pr; until n <> pr*q; pfpotMax[pfMaxIdx] := pot; pfDivCnt *= pot+1; pfSumOfDivs *= (fac-1)DIV(pr-1); inc(pfMaxIdx); end; inc(i); end; pfRemain := n; if n > 1 then Begin pfDivCnt *= 2; pfSumOfDivs *= n+1 end; end; end; function CnvtoBASE(var dgt:tDigits;n:Uint64;base:NativeUint):NativeInt; //n must be multiple of base aka n mod base must be 0 var q,r: Uint64; i : NativeInt; Begin fillchar(dgt,SizeOf(dgt),#0); i := 0; n := n div base; result := 0; repeat r := n; q := n div base; r -= q*base; n := q; dgt[i] := r; inc(i); until (q = 0); //searching lowest pot in base result := 0; while (result<i) AND (dgt[result] = 0) do inc(result); inc(result); end; function IncByBaseInBase(var dgt:tDigits;base:NativeInt):NativeInt; var q :NativeInt; Begin result := 0; q := dgt[result]+1; if q = base then repeat dgt[result] := 0; inc(result); q := dgt[result]+1; until q <> base; dgt[result] := q; result +=1; end; function SieveOneSieve(var pdf:tPrimeDecompField):boolean; var dgt:tDigits; i,j,k,pr,fac,n,MaxP : Uint64; begin n := pdfOfs; if n+SizePrDeFe >= sqr(SmallPrimes[High(SmallPrimes)]) then EXIT(FALSE); //init for i := 0 to SizePrDeFe-1 do begin with pdf[i] do Begin pfDivCnt := 1; pfSumOfDivs := 1; pfRemain := n+i; pfMaxIdx := 0; pfpotPrimIdx[0] := 0; pfpotMax[0] := 0; end; end; //first factor 2. Make n+i even i := (pdfIdx+n) AND 1; IF (n = 0) AND (pdfIdx<2) then i := 2; repeat with pdf[i] do begin j := BsfQWord(n+i); pfMaxIdx := 1; pfpotPrimIdx[0] := 0; pfpotMax[0] := j; pfRemain := (n+i) shr j; pfSumOfDivs := (Uint64(1) shl (j+1))-1; pfDivCnt := j+1; end; i += 2; until i >=SizePrDeFe; //i now index in SmallPrimes i := 0; maxP := trunc(sqrt(n+SizePrDeFe))+1; repeat //search next prime that is in bounds of sieve if n = 0 then begin repeat inc(i); pr := SmallPrimes[i]; k := pr-n MOD pr; if k < SizePrDeFe then break; until pr > MaxP; end else begin repeat inc(i); pr := SmallPrimes[i]; k := pr-n MOD pr; if (k = pr) AND (n>0) then k:= 0; if k < SizePrDeFe then break; until pr > MaxP; end; //no need to use higher primes if pr*pr > n+SizePrDeFe then BREAK; //j is power of prime j := CnvtoBASE(dgt,n+k,pr); repeat with pdf[k] do Begin pfpotPrimIdx[pfMaxIdx] := i; pfpotMax[pfMaxIdx] := j; pfDivCnt *= j+1; fac := pr; repeat pfRemain := pfRemain DIV pr; dec(j); fac *= pr; until j<= 0; pfSumOfDivs *= (fac-1)DIV(pr-1); inc(pfMaxIdx); k += pr; j := IncByBaseInBase(dgt,pr); end; until k >= SizePrDeFe; until false; //correct sum of & count of divisors for i := 0 to High(pdf) do Begin with pdf[i] do begin j := pfRemain; if j <> 1 then begin pfSumOFDivs *= (j+1); pfDivCnt *=2; end; end; end; result := true; end; function NextSieve:boolean; begin dec(pdfIDX,SizePrDeFe); inc(pdfOfs,SizePrDeFe); result := SieveOneSieve(PrimeDecompField); end; function GetNextPrimeDecomp:tpPrimeFac; begin if pdfIDX >= SizePrDeFe then if Not(NextSieve) then EXIT(NIL); result := @PrimeDecompField[pdfIDX]; inc(pdfIDX); end; function Init_Sieve(n:NativeUint):boolean; //Init Sieve pdfIdx,pdfOfs are Global begin pdfIdx := n MOD SizePrDeFe; pdfOfs := n-pdfIdx; result := SieveOneSieve(PrimeDecompField); end; procedure InsertSort(pDiv:tpDivisor; Left, Right : NativeInt ); var I, J: NativeInt; Pivot : tItem; begin for i:= 1 + Left to Right do begin Pivot:= pDiv[i]; j:= i - 1; while (j >= Left) and (pDiv[j] > Pivot) do begin pDiv[j+1]:=pDiv[j]; Dec(j); end; pDiv[j+1]:= pivot; end; end; procedure GetDivisors(pD:tpPrimeFac;var Divs:tDivisors); var pDivs : tpDivisor; pPot : UInt64; i,len,j,l,p,k: Int32; Begin pDivs := @Divs[0]; pDivs[0] := 1; len := 1; l := 1; with pD^ do Begin For i := 0 to pfMaxIdx-1 do begin //Multiply every divisor before with the new primefactors //and append them to the list k := pfpotMax[i]; p := SmallPrimes[pfpotPrimIdx[i]]; pPot :=1; repeat pPot *= p; For j := 0 to len-1 do Begin pDivs[l]:= pPot*pDivs[j]; inc(l); end; dec(k); until k<=0; len := l; end; p := pfRemain; If p >1 then begin For j := 0 to len-1 do Begin pDivs[l]:= p*pDivs[j]; inc(l); end; len := l; end; end; //Sort. Insertsort much faster than QuickSort in this special case InsertSort(pDivs,0,len-1); //end marker pDivs[len] :=0; end; procedure AllFacsOut(var Divs:tdivisors;proper:boolean=true); var k,j: Int32; Begin k := 0; j := 1; if Proper then j:= 2; repeat IF Divs[j] = 0 then BREAK; write(Divs[k],','); inc(j); inc(k); until false; writeln(Divs[k]); end; var pPrimeDecomp :tpPrimeFac; Mypd : tPrimeFac; Divs:tDivisors; T0:Int64; n : NativeUInt; Begin InitSmallPrimes; T0 := GetTickCount64; n := 0; Init_Sieve(0); repeat pPrimeDecomp:= GetNextPrimeDecomp; GetDivisors(pPrimeDecomp,Divs); inc(n); until n > 10*1000*1000+1; T0 := GetTickCount64-T0; writeln('runtime ',T0/1000:0:3,' s'); GetDivisors(pPrimeDecomp,Divs); AllFacsOut(Divs,true); AllFacsOut(Divs,false); writeln('simple version'); T0 := GetTickCount64; n := 0; repeat Mypd:= smplPrimeDecomp(n); GetDivisors(@Mypd,Divs); inc(n); until n > 10*1000*1000+1; T0 := GetTickCount64-T0; writeln('runtime ',T0/1000:0:3,' s'); GetDivisors(@Mypd,Divs); AllFacsOut(Divs,true); AllFacsOut(Divs,false); end.  Output: TIO.RUN //out-commented GetDivisors, but still calculates sum of divisors and count of divisors runtime 0.555 s 1,11,909091 1,11,909091,10000001 simple version runtime 8.167 s 1,11,909091 1,11,909091,10000001 Real time: 8.868 s CPU share: 99.57 % //with GetDivisors runtime 1.815 s 1,11,909091 1,11,909091,10000001 simple version runtime 11.057 s 1,11,909091 1,11,909091,10000001 Real time: 13.082 s CPU share: 99.16 %  ## Perl sub factors { my(n) = @_; return grep { n % _ == 0 }(1 .. n); } print join ' ',factors(64), "\n";  Or more intelligently: sub factors { my n = shift; n = -n if n < 0; my @divisors; for (1 .. int(sqrt(n))) { # faster and less memory than map/grep push @divisors, _ unless n % _; } # Return divisors including top half, without duplicating a square @divisors, map { _*_ == n ? () : int(n/_) } reverse @divisors; } print join " ", factors(64), "\n";  One could also use a module, e.g.: Library: ntheory use ntheory qw/divisors/; print join " ", divisors(12345678), "\n"; # Alternately something like: fordivisors { say } 12345678;  ## Phix There is a builtin factors(n), which takes an optional second parameter to include 1 and n: ?factors(12345,1)  Output: {1,3,5,15,823,2469,4115,12345}  You can find the implementation of factors() and prime_factors() in builtins\pfactors.e ## Phixmonti /# Rosetta Code problem: http://rosettacode.org/wiki/Factors_of_an_integer by Galileo, 05/2022 #/ include ..\Utilitys.pmt def Factors >ps ( ( 1 tps 2 / ) for tps over mod if drop endif endfor ps> ) enddef 11 Factors 21 Factors 32 factors 45 factors 67 factors 96 factors pstack Output: [[1, 11], [1, 3, 7, 21], [1, 2, 4, 8, 16, 32], [1, 3, 5, 9, 15, 45], [1, 67], [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96]] === Press any key to exit === ## PHP function GetFactors(n){ factors = array(1, n); for(i = 2; i * i <= n; i++){ if(n % i == 0){ factors[] = i; if(i * i != n) factors[] = n/i; } } sort(factors); return factors; }  ## Picat ### List comprehension factors(N) = [[D,N // D] : D in 1..N.sqrt.floor, N mod D == 0].flatten.sort_remove_dups. ### Recursion Translation of: Prolog factors2(N,Fs) :- integer(N), N > 0, Fs = findall(F,factors2_(N,F)).sort_remove_dups. factors2_(N,F) :- L = floor(sqrt(N)), between(1,L,X), 0 == N mod X, ( F = X ; F = N // X ). ### Loop using set factors3(N) = Set.keys.sort => Set = new_set(), Set.put(1), Set.put(N), foreach(I in 1..floor(sqrt(N)), N mod I == 0) Set.put(I), Set.put(N//I) end. ### Comparison Let's compare with 18! (6402373705728000) which has 14688 factors. The recursive version is slightly faster than the loop + set version. go => N = 6402373705728000, % factorial(18), println("factors:"), time(_Fs1 = factors(N)) , println("factors2:"), time(factors2(N,_Fs2)), println("factors3:"), time(Fs3=factors3(N)).len), Output: factors: CPU time 3.938 seconds. factors2: CPU time 3.108 seconds. factors3: CPU time 3.159 seconds. ## PicoLisp (de factors (N) (filter '((D) (=0 (% N D))) (range 1 N) ) ) ## PILOT T :Enter a number. A :#n C :factor = 1 T :The factors of #n are: *Loop C :remainder = n % factor T ( remainder = 0 ) :#factor J ( factor = n ) :*Finished C :factor = factor + 1 J :*Loop *Finished END: ## PL/I factors: procedure options(main); declare i binary( 15 )fixed; declare n binary( 15 )fixed; do n = 90 to 100; put skip list( 'factors of: ', n, ': ' ); do i = 1 to n; if mod(n, i) = 0 then put edit( i )(f(4)); end; end; end factors; Output: factors of: 90 : 1 2 3 5 6 9 10 15 18 30 45 90 factors of: 91 : 1 7 13 91 factors of: 92 : 1 2 4 23 46 92 factors of: 93 : 1 3 31 93 factors of: 94 : 1 2 47 94 factors of: 95 : 1 5 19 95 factors of: 96 : 1 2 3 4 6 8 12 16 24 32 48 96 factors of: 97 : 1 97 factors of: 98 : 1 2 7 14 49 98 factors of: 99 : 1 3 9 11 33 99 factors of: 100 : 1 2 4 5 10 20 25 50 100  See also #Polyglot:PL/I and PL/M ## PL/M ## Plain English To run: Start up. Show the factors of 11. Show the factors of 21. Show the factors of 519. Wait for the escape key. Shut down. To show the factors of a number: Write "The factors of " then the number then ":" on the console. Find a square root of the number. Loop. If a counter is past the square root, write "" on the console; exit. Divide the number by the counter giving a quotient and a remainder. If the remainder is 0, show the counter and the quotient. Repeat. A factor is a number. To show a factor and another factor: If the factor is not the other factor, write "" then the factor then " " then the other factor then " " on the console without advancing; exit. Write "" then the factor on the console without advancing. Output: The factors of 11: 1 11 The factors of 21: 1 21 3 7 The factors of 519: 1 519 3 173  ## Polyglot:PL/I and PL/M Works with: 8080 PL/M Compiler ... under CP/M (or an emulator) Should work with many PL/I implementations. The PL/I include file "pg.inc" can be found on the Polyglot:PL/I and PL/M page. Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler. factors_100H: procedure options (main); /* PL/I DEFINITIONS */ %include 'pg.inc'; /* PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. */ /* DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE'; DECLARE SADDR LITERALLY '.', BIT LITERALLY 'BYTE'; DECLARE FIXED LITERALLY ' '; BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END; PRSTRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END; PRCHAR: PROCEDURE( C ); DECLARE C CHARACTER; CALL BDOS( 2, C ); END; PRNL: PROCEDURE; CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END; PRNUMBER: PROCEDURE( N ); DECLARE N ADDRESS; DECLARE V ADDRESS, NSTR( 6 ) BYTE, W BYTE; NSTR( W := LAST( NSTR ) ) = ''; NSTR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 ); DO WHILE( ( V := V / 10 ) > 0 ); NSTR( W := W - 1 ) = '0' + ( V MOD 10 ); END; CALL BDOS( 9, .NSTR( W ) ); END PRNUMBER; MODF: PROCEDURE( A, B )ADDRESS; DECLARE ( A, B )ADDRESS; RETURN( A MOD B ); END MODF; /* END LANGUAGE DEFINITIONS */ /* TASK */ DECLARE ( I, N ) FIXED BINARY; DO N = 90 TO 100; CALL PRSTRING( SADDR( 'FACTORS OF: ' ) ); CALL PRNUMBER( N ); CALL PRCHAR( ':' ); DO I = 1 TO N; IF MODF( N, I ) = 0 THEN DO; CALL PRCHAR( ' ' ); CALL PRNUMBER( I ); END; END; CALL PRNL; END; EOF: end factors_100H; Output: FACTORS OF: 90: 1 2 3 5 6 9 10 15 18 30 45 90 FACTORS OF: 91: 1 7 13 91 FACTORS OF: 92: 1 2 4 23 46 92 FACTORS OF: 93: 1 3 31 93 FACTORS OF: 94: 1 2 47 94 FACTORS OF: 95: 1 5 19 95 FACTORS OF: 96: 1 2 3 4 6 8 12 16 24 32 48 96 FACTORS OF: 97: 1 97 FACTORS OF: 98: 1 2 7 14 49 98 FACTORS OF: 99: 1 3 9 11 33 99 FACTORS OF: 100: 1 2 4 5 10 20 25 50 100  ## PowerShell ### Straightforward but slow function Get-Factor (a) { 1..a | Where-Object { a % _ -eq 0 } }  This one uses a range of integers up to the target number and just filters it using the Where-Object cmdlet. It's very slow though, so it is not very usable for larger numbers. ### A little more clever function Get-Factor (a) { 1..[Math]::Sqrt(a)  | Where-Object { a % _ -eq 0 }  | ForEach-Object { _; a / _ }  | Sort-Object -Unique }  Here the range of integers is only taken up to the square root of the number, the same filtering applies. Afterwards the corresponding larger factors are calculated and sent down the pipeline along with the small ones found earlier. ## ProDOS Uses the math module: editvar /newvar /value=a /userinput=1 /title=Enter an integer: do /delimspaces %% -a- >b printline Factors of -a-: -b- ## Prolog Simple Brute Force Implementation brute_force_factors( N , Fs ) :- integer(N) , N > 0 , setof( F , ( between(1,N,F) , N mod F =:= 0 ) , Fs ) .  A Slightly Smarter Implementation smart_factors(N,Fs) :- integer(N) , N > 0 , setof( F , factor(N,F) , Fs ) . factor(N,F) :- L is floor(sqrt(N)) , between(1,L,X) , 0 =:= N mod X , ( F = X ; F is N // X ) .  Not every Prolog has between/3: you might need this: between(X,Y,Z) :- integer(X) , integer(Y) , X =< Z , between1(X,Y,Z) . between1(X,Y,X) :- X =< Y . between1(X,Y,Z) :- X < Y , X1 is X+1 , between1(X1,Y,Z) .  Output: ?- N=36 ,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ). N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] ; N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] . ?- N=53,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ). N = 53, Factors = [1, 53] ; N = 53, Factors = [1, 53] . ?- N=100,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] ; N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] . ?- N=144,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] ; N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] . ?- N=32765,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32765, Factors = [1, 5, 6553, 32765] ; N = 32765, Factors = [1, 5, 6553, 32765] . ?- N=32766,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] ; N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] . 38 ?- N=32767,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] ; N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] .  ## PureBasic Procedure PrintFactors(n) Protected i, lim=Round(sqr(n),#PB_Round_Up) NewList F.i() For i=1 To lim If n%i=0 AddElement(F()): F()=i AddElement(F()): F()=n/i EndIf Next ;- Present the result SortList(F(),#PB_Sort_Ascending) ForEach F() Print(str(F())+" ") Next EndProcedure If OpenConsole() Print("Enter integer to factorize: ") PrintFactors(Val(Input())) Print(#CRLF+#CRLF+"Press ENTER to quit."): Input() EndIf  Output:  Enter integer to factorize: 96 1 2 3 4 6 8 12 16 24 32 48 96  ## Python Naive and slow but simplest (check all numbers from 1 to n): >>> def factors(n): return [i for i in range(1, n + 1) if not n%i]  Slightly better (realize that there are no factors between n/2 and n): >>> def factors(n): return [i for i in range(1, n//2 + 1) if not n%i] + [n] >>> factors(45) [1, 3, 5, 9, 15, 45]  Much better (realize that factors come in pairs, the smaller of which is no bigger than sqrt(n)): >>> from math import sqrt >>> def factor(n): factors = set() for x in range(1, int(sqrt(n)) + 1): if n % x == 0: factors.add(x) factors.add(n//x) return sorted(factors) >>> for i in (45, 53, 64): print( "%i: factors: %s" % (i, factor(i)) ) 45: factors: [1, 3, 5, 9, 15, 45] 53: factors: [1, 53] 64: factors: [1, 2, 4, 8, 16, 32, 64]  More efficient when factoring many numbers: from itertools import chain, cycle, accumulate # last of which is Python 3 only def factors(n): def prime_powers(n): # c goes through 2, 3, 5, then the infinite (6n+1, 6n+5) series for c in accumulate(chain([2, 1, 2], cycle([2,4]))): if c*c > n: break if n%c: continue d,p = (), c while not n%c: n,p,d = n//c, p*c, d + (p,) yield(d) if n > 1: yield((n,)) r = [1] for e in prime_powers(n): r += [a*b for a in r for b in e] return r  'Task 'Compute the factors of a positive integer. 'These factors are the positive integers by which the number being factored can be divided to yield a positive integer result. Dim Dividendum As Integer, Index As Integer Randomize Timer Dividendum = Int(Rnd * 1000) + 1 Print " Dividendum: "; Dividendum Index = Int(Dividendum / 2) print "Divisors: "; While Index > 0 If Dividendum Mod Index = 0 Then Print Index; " "; Index = Index - 1 Wend End ## Quackery isqrt returns the integer square root and remainder (i.e. the square root of 11 is 3 remainder 2, because three squared plus two equals eleven.) If the number is a perfect square the remainder is zero. This is used to remove a duplicate factor from the list of factors which is generated when finding the factors of a perfect square. The nest editing at the end of the definition (i.e. the code after the drop on a line by itself) removes a duplicate factor if there is one, and arranges the factors in ascending numerical order at the same time.  [ 1 [ 2dup < not while 2 << again ] 0 [ over 1 > while dip [ 2 >> 2dup - ] dup 1 >> unrot - dup 0 < iff drop else [ 2swap nip rot over + ] again ] nip swap ] is isqrt ( n --> n n ) [ [] swap dup isqrt 0 = dip [ times [ dup i^ 1+ /mod iff drop done rot join i^ 1+ join swap ] drop dup size 2 / split ] if [ -1 split drop ] swap join ] is factors ( n --> [ ) 20 times [ i^ 1+ dup dup 10 < if sp echo say ": " factors witheach [ echo i if say ", " ] cr ]  Output:  1: 1 2: 1, 2 3: 1, 3 4: 1, 2, 4 5: 1, 5 6: 1, 2, 3, 6 7: 1, 7 8: 1, 2, 4, 8 9: 1, 3, 9 10: 1, 2, 5, 10 11: 1, 11 12: 1, 2, 3, 4, 6, 12 13: 1, 13 14: 1, 2, 7, 14 15: 1, 3, 5, 15 16: 1, 2, 4, 8, 16 17: 1, 17 18: 1, 2, 3, 6, 9, 18 19: 1, 19 20: 1, 2, 4, 5, 10, 20  ## R ### Array solution factors <- function(n) { if(length(n) > 1) { lapply(as.list(n), factors) } else { one.to.n <- seq_len(n) one.to.n[(n %% one.to.n) == 0] } }  Output: >factors(60) [1] 1 2 3 4 5 6 10 12 15 20 30 60 >factors(c(45, 53, 64)) [[1]] [1] 1 3 5 9 15 45 [[2]] [1] 1 53 [[3]] [1] 1 2 4 8 16 32 64  ### Filter solution With identical output, a more idiomatic way is to use R's Filter. factors <- function(n) c(Filter(function(x) n %% x == 0, seq_len(n %/% 2)), n) #Vectorize is an interesting alternative to the previous solution's lapply. manyFactors <- function(vec) Vectorize(factors)(vec)  ## Racket #lang racket ;; a naive version (define (naive-factors n) (for/list ([i (in-range 1 (add1 n))] #:when (zero? (modulo n i))) i)) (naive-factors 120) ; -> '(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120) ;; much better: use factorize' to get prime factors and construct the ;; list of results from that (require math) (define (factors n) (sort (for/fold ([l '(1)]) ([p (factorize n)]) (append (for*/list ([e (in-range 1 (add1 (cadr p)))] [x l]) (* x (expt (car p) e))) l)) <)) (naive-factors 120) ; -> same ;; to see how fast it is: (define huge 1200034005600070000008900000000000000000) (time (length (factors huge))) ;; I get 42ms for getting a list of 7776 numbers ;; but actually the math library comes with a divisors' function that ;; does the same, except even faster (divisors 120) ; -> same (time (length (divisors huge))) ;; And this one clocks at 17ms  ## Raku (formerly Perl 6) Works with: Rakudo version 2015.12 sub factors (Int n) { (1..n).grep(n %% *) }  ## REALbasic Function factors(num As UInt64) As UInt64() 'This function accepts an unsigned 64 bit integer as input and returns an array of unsigned 64 bit integers Dim result() As UInt64 Dim iFactor As UInt64 = 1 While iFactor <= num/2 'Since a factor will never be larger than half of the number If num Mod iFactor = 0 Then result.Append(iFactor) End If iFactor = iFactor + 1 Wend result.Append(num) 'Since a given number is always a factor of itself Return result End Function  ## Red Red [] factors: function [n [integer!]] [ n: absolute n collect [ repeat i (sq: sqrt n) - 1 [ if n % i = 0 [ keep i keep n / i ] ] if sq = sq: to-integer sq [keep sq] ] ] foreach num [ 24 -64 ; negative 64 ; square 101 ; prime 123456789 ; large ][ print mold/flat sort factors num ]  ## Relation program factors(num) relation fact insert 1 set i = 2 while i < num / 2 if num / i = floor(num/i) insert i end if set i = i + 1 end while insert num print end program ## REXX ### optimized version This REXX version has no effective limits on the number of decimal digits in the number to be factored [by adjusting the number of digits (precision)]. This REXX version also supports negative integers and zero. It also indicates primes in the output listing as well as the number of divisors. It also displays a final count of the number of primes found. This REXX version is about 22% faster than the alternate REXX version (2nd version). /*REXX program displays divisors of any [negative/zero/positive] integer or a range.*/ parse arg LO HI inc . /*obtain the optional args*/ HI= word(HI LO 20, 1); LO= word(LO 1,1); inc= word(inc 1,1) /*define the range options*/ w= length(HI) + 2; numeric digits max(9, w-2); != '∞' /*decimal digits for // */ @.=left('',7); @.1= "{unity}"; @.2= '[prime]'; @.!= " {∞} " /*define some literals. */ say center('n', w) "#divisors" center('divisors', 60) /*display the header. */ say copies('═', w) "═════════" copies('═' , 60) /* " " separator. */ pn= 0 /*count of prime numbers. */ do k=2 until sq.k>=HI; sq.k= k*k /*memoization for squares.*/ end /*k*/ do n=LO to HI by inc; = divs(n); #= words() /*get list of divs; # divs*/ if ==! then do; #= !; = ' (infinite)'; end /*handle case for infinity*/ p= @.#; if n<0 then if n\==-1 then p= @.. /* " " " negative*/ if p==@.2 then pn= pn + 1 /*Prime? Then bump counter*/ say center(n, w) center('['#"]", 9) "──► " p ' '  end /*n*/ /* [↑] process a range of integers. */ say say right(pn, 20) ' primes were found.' /*display the number of primes found. */ exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ divs: procedure expose sq.; parse arg x 1 b; a=1 /*set X and B to the 1st argument. */ if x<2 then do; x= abs(x); if x==1 then return 1; if x==0 then return '∞'; b=x end odd= x // 2 /* [↓] process EVEN or ODD ints. ___*/ do j=2+odd by 1+odd while sq.j<x /*divide by all the integers up to √ x */ if x//j==0 then do; a=a j; b=x%j b; end /*÷? Add divisors to α and ß lists*/ end /*j*/ /* [↑] % ≡ integer division. ___*/ if sq.j==x then return a j b /*Was X a square? Then insert √ x */ return a b /*return the divisors of both lists. */  output when using the input of: -6 200 (Shown at 3/4 size.)  n #divisors divisors ══════ ═════════ ════════════════════════════════════════════════════════════ -6 [4] ──► 1 2 3 6 -5 [2] ──► 1 5 -4 [3] ──► 1 2 4 -3 [2] ──► 1 3 -2 [2] ──► 1 2 -1 [1] ──► {unity} 1 0 [∞] ──► {∞} (infinite) 1 [1] ──► {unity} 1 2 [2] ──► [prime] 1 2 3 [2] ──► [prime] 1 3 4 [3] ──► 1 2 4 5 [2] ──► [prime] 1 5 6 [4] ──► 1 2 3 6 7 [2] ──► [prime] 1 7 8 [4] ──► 1 2 4 8 9 [3] ──► 1 3 9 10 [4] ──► 1 2 5 10 11 [2] ──► [prime] 1 11 12 [6] ──► 1 2 3 4 6 12 13 [2] ──► [prime] 1 13 14 [4] ──► 1 2 7 14 15 [4] ──► 1 3 5 15 16 [5] ──► 1 2 4 8 16 17 [2] ──► [prime] 1 17 18 [6] ──► 1 2 3 6 9 18 19 [2] ──► [prime] 1 19 20 [6] ──► 1 2 4 5 10 20 21 [4] ──► 1 3 7 21 22 [4] ──► 1 2 11 22 23 [2] ──► [prime] 1 23 24 [8] ──► 1 2 3 4 6 8 12 24 25 [3] ──► 1 5 25 26 [4] ──► 1 2 13 26 27 [4] ──► 1 3 9 27 28 [6] ──► 1 2 4 7 14 28 29 [2] ──► [prime] 1 29 30 [8] ──► 1 2 3 5 6 10 15 30 31 [2] ──► [prime] 1 31 32 [6] ──► 1 2 4 8 16 32 33 [4] ──► 1 3 11 33 34 [4] ──► 1 2 17 34 35 [4] ──► 1 5 7 35 36 [9] ──► 1 2 3 4 6 9 12 18 36 37 [2] ──► [prime] 1 37 38 [4] ──► 1 2 19 38 39 [4] ──► 1 3 13 39 40 [8] ──► 1 2 4 5 8 10 20 40 41 [2] ──► [prime] 1 41 42 [8] ──► 1 2 3 6 7 14 21 42 43 [2] ──► [prime] 1 43 44 [6] ──► 1 2 4 11 22 44 45 [6] ──► 1 3 5 9 15 45 46 [4] ──► 1 2 23 46 47 [2] ──► [prime] 1 47 48 [10] ──► 1 2 3 4 6 8 12 16 24 48 49 [3] ──► 1 7 49 50 [6] ──► 1 2 5 10 25 50 51 [4] ──► 1 3 17 51 52 [6] ──► 1 2 4 13 26 52 53 [2] ──► [prime] 1 53 54 [8] ──► 1 2 3 6 9 18 27 54 55 [4] ──► 1 5 11 55 56 [8] ──► 1 2 4 7 8 14 28 56 57 [4] ──► 1 3 19 57 58 [4] ──► 1 2 29 58 59 [2] ──► [prime] 1 59 60 [12] ──► 1 2 3 4 5 6 10 12 15 20 30 60 61 [2] ──► [prime] 1 61 62 [4] ──► 1 2 31 62 63 [6] ──► 1 3 7 9 21 63 64 [7] ──► 1 2 4 8 16 32 64 65 [4] ──► 1 5 13 65 66 [8] ──► 1 2 3 6 11 22 33 66 67 [2] ──► [prime] 1 67 68 [6] ──► 1 2 4 17 34 68 69 [4] ──► 1 3 23 69 70 [8] ──► 1 2 5 7 10 14 35 70 71 [2] ──► [prime] 1 71 72 [12] ──► 1 2 3 4 6 8 9 12 18 24 36 72 73 [2] ──► [prime] 1 73 74 [4] ──► 1 2 37 74 75 [6] ──► 1 3 5 15 25 75 76 [6] ──► 1 2 4 19 38 76 77 [4] ──► 1 7 11 77 78 [8] ──► 1 2 3 6 13 26 39 78 79 [2] ──► [prime] 1 79 80 [10] ──► 1 2 4 5 8 10 16 20 40 80 81 [5] ──► 1 3 9 27 81 82 [4] ──► 1 2 41 82 83 [2] ──► [prime] 1 83 84 [12] ──► 1 2 3 4 6 7 12 14 21 28 42 84 85 [4] ──► 1 5 17 85 86 [4] ──► 1 2 43 86 87 [4] ──► 1 3 29 87 88 [8] ──► 1 2 4 8 11 22 44 88 89 [2] ──► [prime] 1 89 90 [12] ──► 1 2 3 5 6 9 10 15 18 30 45 90 91 [4] ──► 1 7 13 91 92 [6] ──► 1 2 4 23 46 92 93 [4] ──► 1 3 31 93 94 [4] ──► 1 2 47 94 95 [4] ──► 1 5 19 95 96 [12] ──► 1 2 3 4 6 8 12 16 24 32 48 96 97 [2] ──► [prime] 1 97 98 [6] ──► 1 2 7 14 49 98 99 [6] ──► 1 3 9 11 33 99 100 [9] ──► 1 2 4 5 10 20 25 50 100 101 [2] ──► [prime] 1 101 102 [8] ──► 1 2 3 6 17 34 51 102 103 [2] ──► [prime] 1 103 104 [8] ──► 1 2 4 8 13 26 52 104 105 [8] ──► 1 3 5 7 15 21 35 105 106 [4] ──► 1 2 53 106 107 [2] ──► [prime] 1 107 108 [12] ──► 1 2 3 4 6 9 12 18 27 36 54 108 109 [2] ──► [prime] 1 109 110 [8] ──► 1 2 5 10 11 22 55 110 111 [4] ──► 1 3 37 111 112 [10] ──► 1 2 4 7 8 14 16 28 56 112 113 [2] ──► [prime] 1 113 114 [8] ──► 1 2 3 6 19 38 57 114 115 [4] ──► 1 5 23 115 116 [6] ──► 1 2 4 29 58 116 117 [6] ──► 1 3 9 13 39 117 118 [4] ──► 1 2 59 118 119 [4] ──► 1 7 17 119 120 [16] ──► 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 121 [3] ──► 1 11 121 122 [4] ──► 1 2 61 122 123 [4] ──► 1 3 41 123 124 [6] ──► 1 2 4 31 62 124 125 [4] ──► 1 5 25 125 126 [12] ──► 1 2 3 6 7 9 14 18 21 42 63 126 127 [2] ──► [prime] 1 127 128 [8] ──► 1 2 4 8 16 32 64 128 129 [4] ──► 1 3 43 129 130 [8] ──► 1 2 5 10 13 26 65 130 131 [2] ──► [prime] 1 131 132 [12] ──► 1 2 3 4 6 11 12 22 33 44 66 132 133 [4] ──► 1 7 19 133 134 [4] ──► 1 2 67 134 135 [8] ──► 1 3 5 9 15 27 45 135 136 [8] ──► 1 2 4 8 17 34 68 136 137 [2] ──► [prime] 1 137 138 [8] ──► 1 2 3 6 23 46 69 138 139 [2] ──► [prime] 1 139 140 [12] ──► 1 2 4 5 7 10 14 20 28 35 70 140 141 [4] ──► 1 3 47 141 142 [4] ──► 1 2 71 142 143 [4] ──► 1 11 13 143 144 [15] ──► 1 2 3 4 6 8 9 12 16 18 24 36 48 72 144 145 [4] ──► 1 5 29 145 146 [4] ──► 1 2 73 146 147 [6] ──► 1 3 7 21 49 147 148 [6] ──► 1 2 4 37 74 148 149 [2] ──► [prime] 1 149 150 [12] ──► 1 2 3 5 6 10 15 25 30 50 75 150 151 [2] ──► [prime] 1 151 152 [8] ──► 1 2 4 8 19 38 76 152 153 [6] ──► 1 3 9 17 51 153 154 [8] ──► 1 2 7 11 14 22 77 154 155 [4] ──► 1 5 31 155 156 [12] ──► 1 2 3 4 6 12 13 26 39 52 78 156 157 [2] ──► [prime] 1 157 158 [4] ──► 1 2 79 158 159 [4] ──► 1 3 53 159 160 [12] ──► 1 2 4 5 8 10 16 20 32 40 80 160 161 [4] ──► 1 7 23 161 162 [10] ──► 1 2 3 6 9 18 27 54 81 162 163 [2] ──► [prime] 1 163 164 [6] ──► 1 2 4 41 82 164 165 [8] ──► 1 3 5 11 15 33 55 165 166 [4] ──► 1 2 83 166 167 [2] ──► [prime] 1 167 168 [16] ──► 1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168 169 [3] ──► 1 13 169 170 [8] ──► 1 2 5 10 17 34 85 170 171 [6] ──► 1 3 9 19 57 171 172 [6] ──► 1 2 4 43 86 172 173 [2] ──► [prime] 1 173 174 [8] ──► 1 2 3 6 29 58 87 174 175 [6] ──► 1 5 7 25 35 175 176 [10] ──► 1 2 4 8 11 16 22 44 88 176 177 [4] ──► 1 3 59 177 178 [4] ──► 1 2 89 178 179 [2] ──► [prime] 1 179 180 [18] ──► 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 181 [2] ──► [prime] 1 181 182 [8] ──► 1 2 7 13 14 26 91 182 183 [4] ──► 1 3 61 183 184 [8] ──► 1 2 4 8 23 46 92 184 185 [4] ──► 1 5 37 185 186 [8] ──► 1 2 3 6 31 62 93 186 187 [4] ──► 1 11 17 187 188 [6] ──► 1 2 4 47 94 188 189 [8] ──► 1 3 7 9 21 27 63 189 190 [8] ──► 1 2 5 10 19 38 95 190 191 [2] ──► [prime] 1 191 192 [14] ──► 1 2 3 4 6 8 12 16 24 32 48 64 96 192 193 [2] ──► [prime] 1 193 194 [4] ──► 1 2 97 194 195 [8] ──► 1 3 5 13 15 39 65 195 196 [9] ──► 1 2 4 7 14 28 49 98 196 197 [2] ──► [prime] 1 197 198 [12] ──► 1 2 3 6 9 11 18 22 33 66 99 198 199 [2] ──► [prime] 1 199 200 [12] ──► 1 2 4 5 8 10 20 25 40 50 100 200 46 primes were found.  ### Alternate Version Translation of: REXX optimized version /* REXX *************************************************************** * Program to calculate and show divisors of positive integer(s). * 03.08.2012 Walter Pachl simplified the above somewhat * in particular I see no benefit from divAdd procedure * 04.08.2012 the reference to 'above' is no longer valid since that * was meanwhile changed for the better. * 04.08.2012 took over some improvements from new above **********************************************************************/ Parse arg low high . Select When low='' Then Parse Value '1 200' with low high When high='' Then high=low Otherwise Nop End do j=low to high say ' n = ' right(j,6) " divisors = " divs(j) end exit divs: procedure; parse arg x if x==1 then return 1 /*handle special case of 1 */ Parse Value '1' x With lo hi /*initialize lists: lo=1 hi=x */ odd=x//2 /* 1 if x is odd */ Do j=2+odd By 1+odd While j*j<x /*divide by numbers<sqrt(x) */ if x//j==0 then Do /*Divisible? Add two divisors:*/ lo=lo j /* list low divisors */ hi=x%j hi /* list high divisors */ End End If j*j=x Then /*for a square number as input */ lo=lo j /* add its square root */ return lo hi /* return both lists */  output when using the default input: (Shown at 3/4 size.)  n = 1 divisors = 1 n = 2 divisors = 1 2 n = 3 divisors = 1 3 n = 4 divisors = 1 2 4 n = 5 divisors = 1 5 n = 6 divisors = 1 2 3 6 n = 7 divisors = 1 7 n = 8 divisors = 1 2 4 8 n = 9 divisors = 1 3 9 n = 10 divisors = 1 2 5 10 n = 11 divisors = 1 11 n = 12 divisors = 1 2 3 4 6 12 n = 13 divisors = 1 13 n = 14 divisors = 1 2 7 14 n = 15 divisors = 1 3 5 15 n = 16 divisors = 1 2 4 8 16 n = 17 divisors = 1 17 n = 18 divisors = 1 2 3 6 9 18 n = 19 divisors = 1 19 n = 20 divisors = 1 2 4 5 10 20 n = 21 divisors = 1 3 7 21 n = 22 divisors = 1 2 11 22 n = 23 divisors = 1 23 n = 24 divisors = 1 2 3 4 6 8 12 24 n = 25 divisors = 1 5 25 n = 26 divisors = 1 2 13 26 n = 27 divisors = 1 3 9 27 n = 28 divisors = 1 2 4 7 14 28 n = 29 divisors = 1 29 n = 30 divisors = 1 2 3 5 6 10 15 30 n = 31 divisors = 1 31 n = 32 divisors = 1 2 4 8 16 32 n = 33 divisors = 1 3 11 33 n = 34 divisors = 1 2 17 34 n = 35 divisors = 1 5 7 35 n = 36 divisors = 1 2 3 4 6 9 12 18 36 n = 37 divisors = 1 37 n = 38 divisors = 1 2 19 38 n = 39 divisors = 1 3 13 39 n = 40 divisors = 1 2 4 5 8 10 20 40 n = 41 divisors = 1 41 n = 42 divisors = 1 2 3 6 7 14 21 42 n = 43 divisors = 1 43 n = 44 divisors = 1 2 4 11 22 44 n = 45 divisors = 1 3 5 9 15 45 n = 46 divisors = 1 2 23 46 n = 47 divisors = 1 47 n = 48 divisors = 1 2 3 4 6 8 12 16 24 48 n = 49 divisors = 1 7 49 n = 50 divisors = 1 2 5 10 25 50 n = 51 divisors = 1 3 17 51 n = 52 divisors = 1 2 4 13 26 52 n = 53 divisors = 1 53 n = 54 divisors = 1 2 3 6 9 18 27 54 n = 55 divisors = 1 5 11 55 n = 56 divisors = 1 2 4 7 8 14 28 56 n = 57 divisors = 1 3 19 57 n = 58 divisors = 1 2 29 58 n = 59 divisors = 1 59 n = 60 divisors = 1 2 3 4 5 6 10 12 15 20 30 60 n = 61 divisors = 1 61 n = 62 divisors = 1 2 31 62 n = 63 divisors = 1 3 7 9 21 63 n = 64 divisors = 1 2 4 8 16 32 64 n = 65 divisors = 1 5 13 65 n = 66 divisors = 1 2 3 6 11 22 33 66 n = 67 divisors = 1 67 n = 68 divisors = 1 2 4 17 34 68 n = 69 divisors = 1 3 23 69 n = 70 divisors = 1 2 5 7 10 14 35 70 n = 71 divisors = 1 71 n = 72 divisors = 1 2 3 4 6 8 9 12 18 24 36 72 n = 73 divisors = 1 73 n = 74 divisors = 1 2 37 74 n = 75 divisors = 1 3 5 15 25 75 n = 76 divisors = 1 2 4 19 38 76 n = 77 divisors = 1 7 11 77 n = 78 divisors = 1 2 3 6 13 26 39 78 n = 79 divisors = 1 79 n = 80 divisors = 1 2 4 5 8 10 16 20 40 80 n = 81 divisors = 1 3 9 27 81 n = 82 divisors = 1 2 41 82 n = 83 divisors = 1 83 n = 84 divisors = 1 2 3 4 6 7 12 14 21 28 42 84 n = 85 divisors = 1 5 17 85 n = 86 divisors = 1 2 43 86 n = 87 divisors = 1 3 29 87 n = 88 divisors = 1 2 4 8 11 22 44 88 n = 89 divisors = 1 89 n = 90 divisors = 1 2 3 5 6 9 10 15 18 30 45 90 n = 91 divisors = 1 7 13 91 n = 92 divisors = 1 2 4 23 46 92 n = 93 divisors = 1 3 31 93 n = 94 divisors = 1 2 47 94 n = 95 divisors = 1 5 19 95 n = 96 divisors = 1 2 3 4 6 8 12 16 24 32 48 96 n = 97 divisors = 1 97 n = 98 divisors = 1 2 7 14 49 98 n = 99 divisors = 1 3 9 11 33 99 n = 100 divisors = 1 2 4 5 10 20 25 50 100 n = 101 divisors = 1 101 n = 102 divisors = 1 2 3 6 17 34 51 102 n = 103 divisors = 1 103 n = 104 divisors = 1 2 4 8 13 26 52 104 n = 105 divisors = 1 3 5 7 15 21 35 105 n = 106 divisors = 1 2 53 106 n = 107 divisors = 1 107 n = 108 divisors = 1 2 3 4 6 9 12 18 27 36 54 108 n = 109 divisors = 1 109 n = 110 divisors = 1 2 5 10 11 22 55 110 n = 111 divisors = 1 3 37 111 n = 112 divisors = 1 2 4 7 8 14 16 28 56 112 n = 113 divisors = 1 113 n = 114 divisors = 1 2 3 6 19 38 57 114 n = 115 divisors = 1 5 23 115 n = 116 divisors = 1 2 4 29 58 116 n = 117 divisors = 1 3 9 13 39 117 n = 118 divisors = 1 2 59 118 n = 119 divisors = 1 7 17 119 n = 120 divisors = 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 n = 121 divisors = 1 11 121 n = 122 divisors = 1 2 61 122 n = 123 divisors = 1 3 41 123 n = 124 divisors = 1 2 4 31 62 124 n = 125 divisors = 1 5 25 125 n = 126 divisors = 1 2 3 6 7 9 14 18 21 42 63 126 n = 127 divisors = 1 127 n = 128 divisors = 1 2 4 8 16 32 64 128 n = 129 divisors = 1 3 43 129 n = 130 divisors = 1 2 5 10 13 26 65 130 n = 131 divisors = 1 131 n = 132 divisors = 1 2 3 4 6 11 12 22 33 44 66 132 n = 133 divisors = 1 7 19 133 n = 134 divisors = 1 2 67 134 n = 135 divisors = 1 3 5 9 15 27 45 135 n = 136 divisors = 1 2 4 8 17 34 68 136 n = 137 divisors = 1 137 n = 138 divisors = 1 2 3 6 23 46 69 138 n = 139 divisors = 1 139 n = 140 divisors = 1 2 4 5 7 10 14 20 28 35 70 140 n = 141 divisors = 1 3 47 141 n = 142 divisors = 1 2 71 142 n = 143 divisors = 1 11 13 143 n = 144 divisors = 1 2 3 4 6 8 9 12 16 18 24 36 48 72 144 n = 145 divisors = 1 5 29 145 n = 146 divisors = 1 2 73 146 n = 147 divisors = 1 3 7 21 49 147 n = 148 divisors = 1 2 4 37 74 148 n = 149 divisors = 1 149 n = 150 divisors = 1 2 3 5 6 10 15 25 30 50 75 150 n = 151 divisors = 1 151 n = 152 divisors = 1 2 4 8 19 38 76 152 n = 153 divisors = 1 3 9 17 51 153 n = 154 divisors = 1 2 7 11 14 22 77 154 n = 155 divisors = 1 5 31 155 n = 156 divisors = 1 2 3 4 6 12 13 26 39 52 78 156 n = 157 divisors = 1 157 n = 158 divisors = 1 2 79 158 n = 159 divisors = 1 3 53 159 n = 160 divisors = 1 2 4 5 8 10 16 20 32 40 80 160 n = 161 divisors = 1 7 23 161 n = 162 divisors = 1 2 3 6 9 18 27 54 81 162 n = 163 divisors = 1 163 n = 164 divisors = 1 2 4 41 82 164 n = 165 divisors = 1 3 5 11 15 33 55 165 n = 166 divisors = 1 2 83 166 n = 167 divisors = 1 167 n = 168 divisors = 1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168 n = 169 divisors = 1 13 169 n = 170 divisors = 1 2 5 10 17 34 85 170 n = 171 divisors = 1 3 9 19 57 171 n = 172 divisors = 1 2 4 43 86 172 n = 173 divisors = 1 173 n = 174 divisors = 1 2 3 6 29 58 87 174 n = 175 divisors = 1 5 7 25 35 175 n = 176 divisors = 1 2 4 8 11 16 22 44 88 176 n = 177 divisors = 1 3 59 177 n = 178 divisors = 1 2 89 178 n = 179 divisors = 1 179 n = 180 divisors = 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 n = 181 divisors = 1 181 n = 182 divisors = 1 2 7 13 14 26 91 182 n = 183 divisors = 1 3 61 183 n = 184 divisors = 1 2 4 8 23 46 92 184 n = 185 divisors = 1 5 37 185 n = 186 divisors = 1 2 3 6 31 62 93 186 n = 187 divisors = 1 11 17 187 n = 188 divisors = 1 2 4 47 94 188 n = 189 divisors = 1 3 7 9 21 27 63 189 n = 190 divisors = 1 2 5 10 19 38 95 190 n = 191 divisors = 1 191 n = 192 divisors = 1 2 3 4 6 8 12 16 24 32 48 64 96 192 n = 193 divisors = 1 193 n = 194 divisors = 1 2 97 194 n = 195 divisors = 1 3 5 13 15 39 65 195 n = 196 divisors = 1 2 4 7 14 28 49 98 196 n = 197 divisors = 1 197 n = 198 divisors = 1 2 3 6 9 11 18 22 33 66 99 198 n = 199 divisors = 1 199 n = 200 divisors = 1 2 4 5 8 10 20 25 40 50 100 200  ## Ring nArray = list(100) n = 45 j = 0 for i = 1 to n if n % i = 0 j = j + 1 nArray[j] = i ok next see "Factors of " + n + " = " for i = 1 to j see "" + nArray[i] + " " next ## Ruby class Integer def factors() (1..self).select { |n| (self % n).zero? } end end p 45.factors  [1, 3, 5, 9, 15, 45]  As we only have to loop up to ${\displaystyle \sqrt{n}}$, we can write class Integer def factors 1.upto(Integer.sqrt(self)).select {|i| (self % i).zero?}.inject([]) do |f, i| f << self/i unless i == self/i f << i end.sort end end [45, 53, 64].each {|n| puts "#{n} : #{n.factors}"}  Output: 45 : [1, 3, 5, 9, 15, 45] 53 : [1, 53] 64 : [1, 2, 4, 8, 16, 32, 64] ### Using the prime library require 'prime' def factors m return [1] if 1==m primes, powers = Prime.prime_division(m).transpose ranges = powers.map{|n| (0..n).to_a} ranges[0].product( *ranges[1..-1] ). map{|es| primes.zip(es).map{|p,e| p**e}.reduce :*}. sort end [1, 7, 45, 100].each{|n| p factors n}  Output: [1] [1, 7] [1, 3, 5, 9, 15, 45] [1, 2, 4, 5, 10, 20, 25, 50, 100]  ## Run BASIC PRINT "Factors of 45 are ";factorlist(45) PRINT "Factors of 12345 are "; factorlist(12345) END function factorlist(f) DIM L(100) FOR i = 1 TO SQR(f) IF (f MOD i) = 0 THEN L(c) = i c = c + 1 IF (f <> i^2) THEN L(c) = (f / i) c = c + 1 END IF END IF NEXT i s = 1 while s = 1 s = 0 for i = 0 to c-1 if L(i) > L(i+1) and L(i+1) <> 0 then t = L(i) L(i) = L(i+1) L(i+1) = t s = 1 end if next i wend FOR i = 0 TO c-1 factorlist = factorlist + STR(L(i)) + ", " NEXT end function Output: Factors of 45 are 1, 3, 5, 9, 15, 45, Factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345,  ## Rust fn main() { assert_eq!(vec![1, 2, 4, 5, 10, 10, 20, 25, 50, 100], factor(100)); // asserts that two expressions are equal to each other assert_eq!(vec![1, 101], factor(101)); } fn factor(num: i32) -> Vec<i32> { let mut factors: Vec<i32> = Vec::new(); // creates a new vector for the factors of the number for i in 1..((num as f32).sqrt() as i32 + 1) { if num % i == 0 { factors.push(i); // pushes smallest factor to factors factors.push(num/i); // pushes largest factor to factors } } factors.sort(); // sorts the factors into numerical order for viewing purposes factors // returns the factors }  Alternative functional version: fn factor(n: i32) -> Vec<i32> { (1..=n).filter(|i| n % i == 0).collect() }  ## Sather class MAIN is factors!(n :INT):INT is yield 1; loop i ::= 2.upto!( n.flt.sqrt.int ); if n%i = 0 then yield i; if (i*i) /= n then yield n / i; end; end; end; yield n; end; main is a :ARRAY{INT} := |3135, 45, 64, 53, 45, 81|; loop l ::= a.elt!; #OUT + "factors of " + l + ": "; loop ri ::= factors!(l); #OUT + ri + " "; end; #OUT + "\n"; end; end; end; ## Scala Brute force approach: def factors(num: Int) = { (1 to num).filter { divisor => num % divisor == 0 } }  Brute force until sqrt(num) is enough, the code above can be edited as follows (Scala 3 enabled) def factors(num: Int) = { val list = (1 to math.sqrt(num).floor.toInt).filter(num % _ == 0) list ++ list.reverse.dropWhile(d => d*d == num).map(num / _) }  ## Scheme This implementation uses a naive trial division algorithm. (define (factors n) (define (*factors d) (cond ((> d n) (list)) ((= (modulo n d) 0) (cons d (*factors (+ d 1)))) (else (*factors (+ d 1))))) (*factors 1)) (display (factors 1111111)) (newline)  Output:  (1 239 4649 1111111)  ## Seed7  include "seed7_05.s7i"; const proc: writeFactors (in integer: number) is func local var integer: testNum is 0; begin write("Factors of " <& number <& ": "); for testNum range 1 to sqrt(number) do if number rem testNum = 0 then if testNum <> 1 then write(", "); end if; write(testNum); if testNum <> number div testNum then write(", " <& number div testNum); end if; end if; end for; writeln; end func; const proc: main is func local const array integer: numsToFactor is [] (45, 53, 64); var integer: number is 0; begin for number range numsToFactor do writeFactors(number); end for; end func; Output: Factors of 45: 1, 45, 3, 15, 5, 9 Factors of 53: 1, 53 Factors of 64: 1, 64, 2, 32, 4, 16, 8  ## SequenceL Brute Force Method A simple brute force method using an indexed partial function as a filter. Factors(num(0))[i] := i when num mod i = 0 foreach i within 1 ... num; Slightly More Efficient Method A slightly more efficient method, only going up to the sqrt(n). Factors(num(0)) := let factorPairs[i] := [i] when i = sqrt(num) else [i, num/i] when num mod i = 0 foreach i within 1 ... floor(sqrt(num)); in join(factorPairs); ## Sidef Built-in: say divisors(97) #=> [1, 97] say divisors(2695) #=> [1, 5, 7, 11, 35, 49, 55, 77, 245, 385, 539, 2695]  Trial-division (slow for large n): func divisors(n) { gather { { |d| take(d, n//d) if d.divides(n) } << 1..n.isqrt }.sort.uniq } [53, 64, 32766].each {|n| say "divisors(#{n}): #{divisors(n)}" }  Output: divisors(53): [1, 53] divisors(64): [1, 2, 4, 8, 16, 32, 64] divisors(32766): [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766]  ## Slate n@(Integer traits) primeFactors [ [| :result | result nextPut: 1. n primesDo: [| :prime | result nextPut: prime]] writingAs: {} ]. where primesDo: is a part of the standard numerics library: n@(Integer traits) primesDo: block "Decomposes the Integer into primes, applying the block to each (in increasing order)." [| div next remaining | div: 2. next: 3. remaining: n. [[(remaining \\ div) isZero] whileTrue: [block applyTo: {div}. remaining: remaining // div]. remaining = 1] whileFalse: [div: next. next: next + 2] "Just looks at the next odd integer." ]. ## Smalltalk Copied from the Python example, but code added to the Integer built in class: Integer>>factors | a | a := OrderedCollection new. 1 to: (self / 2) do: [ :i | ((self \\ i) = 0) ifTrue: [ a add: i ] ]. a add: self. ^a  Then use as follows: 59 factors -> an OrderedCollection(1 59) 120 factors -> an OrderedCollection(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120)  ## Standard ML Need to print the list because Standard ML truncates the display of longer returned lists. fun printIntList ls = ( List.app (fn n => print(Int.toString n ^ " ")) ls; print "\n" ); fun factors n = let fun factors'(n, k) = if k > n then [] else if n mod k = 0 then k :: factors'(n, k+1) else factors'(n, k+1) in factors'(n,1) end; Call: printIntList(factors 12345) printIntList(factors 120) Output: 1 3 5 15 823 2469 4115 12345 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60  ## Swift Simple implementation: func factors(n: Int) -> [Int] { return filter(1...n) { n % 0 == 0 } }  More efficient implementation: import func Darwin.sqrt func sqrt(x:Int) -> Int { return Int(sqrt(Double(x))) } func factors(n: Int) -> [Int] { var result = [Int]() for factor in filter (1...sqrt(n), { n % 0 == 0 }) { result.append(factor) if n/factor != factor { result.append(n/factor) } } return sorted(result) }  Call: println(factors(4)) println(factors(1)) println(factors(25)) println(factors(63)) println(factors(19)) println(factors(768))  Output: [1, 2, 4] [1] [1, 5, 25] [1, 3, 7, 9, 21, 63] [1, 19] [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768]  ## Tailspin [1..351 -> \(when <?(351 mod  <=0>)> do !] -> !OUT::write
Output:
[1, 3, 9, 13, 27, 39, 117, 351]


## Tcl

proc factors {n} {
set factors {}
for {set i 1} {$i <= sqrt($n)} {incr i} {
if {$n %$i == 0} {
lappend factors $i [expr {$n / $i}] } } return [lsort -unique -integer$factors]
}
puts [factors 64]
puts [factors 45]
puts [factors 53]

Output:
1 2 4 8 16 32 64
1 3 5 9 15 45
1 53

## UNIX Shell

This should work in all Bourne-compatible shells, assuming the system has both sort and at least one of bc or dc.

factor() {
r=echo "sqrt($1)" | bc # or echo$1 v p | dc
i=1
while [ $i -lt$r ]; do
if [ expr $1 %$i -eq 0 ]; then
echo $i expr$1 / $i fi i=expr$i + 1
done | sort -nu
}


## Ursa

This program takes an integer from the command line and outputs its factors.

decl int n
set n (int args<1>)

decl int i
for (set i 1) (< i (+ (/ n 2) 1)) (inc i)
if (= (mod n i) 0)
out i "  " console
end if
end for
out n endl console

## Ursala

The simple way:

#import std
#import nat

factors "n" = (filter not remainder/"n") nrange(1,"n")

The complicated way:

factors "n" = nleq-<&@s <.~&r,quotient>*= "n"-* (not remainder/"n")*~ nrange(1,root("n",2))

Another idea would be to approximate an upper bound for the square root of "n" with some bit twiddling such as &!*K31 "n", which evaluates to a binary number of all 1's half the width of "n" rounded up, and another would be to use the division function to get the quotient and remainder at the same time. Combining these ideas, losing the dummy variable, and cleaning up some other cruft, we have

factors = nleq-<&@rrZPFLs+ ^(~&r,division)^*D/~& nrange/1+ &!*K31

where nleq-<& isn't strictly necessary unless an ordered list is required.

#cast %nL

example = factors 100
Output:
<1,2,4,5,10,20,25,50,100>

## VBA

Function Factors(x As Integer) As String
Application.Volatile
Dim i As Integer
Dim cooresponding_factors As String
Factors = 1
corresponding_factors = x
For i = 2 To Sqr(x)
If x Mod i = 0 Then
Factors = Factors & ", " & i
If i <> x / i Then corresponding_factors = x / i & ", " & corresponding_factors
End If
Next i
If x <> 1 Then Factors = Factors & ", " & corresponding_factors
End Function

Output:
cell formula is "=Factors(840)"
resultant value is "1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840"

## Verilog

module main;
integer i, n;

initial begin
n = 45;

$write(n, " =>"); for(i = 1; i <= n / 2; i = i + 1) if(n % i == 0)$write(i);
$display(n);$finish ;
end
endmodule

Output:
         45 =>          1          3          5          9         15         45


## Wortel

@let {
factors1      &n !-\%%n @to n
factors_tacit @(\\%% !- @to)
[[
!factors1 10
!factors_tacit 100
!factors1 720
]]
}
Returns:
[
[1 2 5 10]
[1 2 4 5 10 20 25 50 100]
[1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720]
]

## Wren

Library: Wren-fmt
Library: Wren-math
import "/fmt" for Fmt
import "/math" for Int

var a = [11, 21, 32, 45, 67, 96, 159, 723, 1024, 5673, 12345, 32767, 123459, 999997]
System.print("The factors of the following numbers are:")
for (e in a) System.print("%(Fmt.d(6, e)) => %(Int.divisors(e))")

Output:
The factors of the following numbers are:
11 => [1, 11]
21 => [1, 3, 7, 21]
32 => [1, 2, 4, 8, 16, 32]
45 => [1, 3, 5, 9, 15, 45]
67 => [1, 67]
96 => [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96]
159 => [1, 3, 53, 159]
723 => [1, 3, 241, 723]
1024 => [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]
5673 => [1, 3, 31, 61, 93, 183, 1891, 5673]
12345 => [1, 3, 5, 15, 823, 2469, 4115, 12345]
32767 => [1, 7, 31, 151, 217, 1057, 4681, 32767]
123459 => [1, 3, 7, 21, 5879, 17637, 41153, 123459]
999997 => [1, 757, 1321, 999997]


## X86 Assembly

Works with: nasm
section .bss
factorArr resd 250 ;big buffer against seg fault

section .text
global _main
_main:
mov ebp, esp; for correct debugging
mov eax, 0x7ffffffe ;number of which we want to know the factors, max num this program works with
mov ebx, eax ;save eax
mov ecx, 1 ;n, factor we test for
mov [factorArr], dword 0
looping:
mov eax, ebx ;restore eax
xor edx, edx ;clear edx
div ecx
cmp edx, 0 ;test if our number % n == 0
jne next
mov edx, [factorArr] ;if yes, we increment the size of the array and append n
inc edx
mov [factorArr+edx*4], ecx ;appending n
mov [factorArr], edx ;storing the new size
next:
mov eax, ecx
cmp eax, ebx ;is n bigger then our number ?
jg end ;if yes we end
inc ecx
jmp looping
end:
mov ecx, factorArr ;pass arr address by ecx
xor eax, eax ;clear eax
mov esp, ebp ;garbage collecting
ret


## 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;
]
Output:
1 = 1
2 = 2
3 = 3
4 = 2 * 2
5 = 5
6 = 2 * 3
7 = 7
8 = 2 * 2 * 2
9 = 3 * 3
10 = 2 * 5
11 = 11
12 = 2 * 2 * 3
13 = 13
14 = 2 * 7
15 = 3 * 5
16 = 2 * 2 * 2 * 2
17 = 17
18 = 2 * 3 * 3
. . .
57086 = 2 * 17 * 23 * 73
57087 = 3 * 3 * 6343
57088 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 223
57089 = 57089
57090 = 2 * 3 * 5 * 11 * 173
57091 = 37 * 1543
57092 = 2 * 2 * 7 * 2039
57093 = 3 * 19031
57094 = 2 * 28547
57095 = 5 * 19 * 601
57096 = 2 * 2 * 2 * 3 * 3 * 13 * 61
57097 = 57097


## Yabasic

Translation of: FreeBASIC
sub printFactors(n)
if n < 1 then return 0 : fi
print n, " =>",
for i = 1 to n / 2
if mod(n, i) = 0 then print i, "  "; : fi
next i
print n
end sub

printFactors(11)
printFactors(21)
printFactors(32)
printFactors(45)
printFactors(67)
printFactors(96)
print
end
Output:
Igual que la entrada de FreeBASIC.


## zkl

Translation of: Chapel
fcn f(n){ (1).pump(n.toFloat().sqrt(), List,
'wrap(m){((n % m)==0) and T(m,n/m) or Void.Skip}) }
fcn g(n){ [[(m); [1..n.toFloat().sqrt()],'{n%m==0}; '{T(m,n/m)} ]] }  // list comprehension
Output:
zkl: f(45)
L(L(1,45),L(3,15),L(5,9))

zkl: g(45)
L(L(1,45),L(3,15),L(5,9))


## ZX Spectrum Basic

Translation of: AWK
10 INPUT "Enter a number or 0 to exit: ";n
20 IF n=0 THEN STOP
30 PRINT "Factors of ";n;": ";
40 FOR i=1 TO n
50 IF FN m(n,i)=0 THEN PRINT i;" ";
60 NEXT i
70 DEF FN m(a,b)=a-INT (a/b)*b