Prolog (SWI), 61 bytes

0+1. N+F:-nth1(N,_,_),Y is N-1,Y+G,(F is G*N->1>0;F<G,!,0>1). 

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Steffan's answer is much shorter at 28 bytes, but this predicate was created to be as general as possible. It can be used to:

• Validate that N! = F (for example, 5+120 will succeed, 6+120 will fail)
• Calculate N! (5+F will bind F to 120)
• Calculate N from N! (N+120 will bind N to 5)
  • N+1 has both 0 and 1 as possible values
  • A non-factorial will fail the predicate
• Generate all N, N! pairs

The last section feels like it can be golfed, especially as it has both 0>1 as always true and 0<1 as always false, but I've been staring at it for a while and can't figure out anything better. Pity that \+! doesn't work.

Brain-Flak, 52 bytes

<>(())<>{(({}[()]))({<>({})<><({}[()])>}{}<>{})<>}<> 

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Posting my own Brain-Flak solution, which differs from the same size one from the older challenge.

Befunge-93, 20 19 bytes

&+#v:!_: \@#<*_\:.# 

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Reposting more of my answers from the old challenge that didn't fit the requirements. This one didn't get up to 125!, at least with this interpreter.

Explanation:

& Get the input + Add it to the current counter (initially 0) :!_ Duplicate and check if it is zero &+ : If not, duplicate and repeat, but add the -1 from EOF to the input #v:! If it is, not the 0 into a 1, duplicate and go to the second line This initialises the stack as n,n-1,n-2...,1,1,1 < Start going left \ _ : Check if the second element on the stack is zero * If not, then multiply the top two elements @# \ .# If it is, then print the factorial value and terminate 

I believe this was actually my first answer on this site, with the below being the 20 byte version of the above.

Befunge-93, 20 bytes

1&0>-#1:__\#0:#*_$.@ 

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Funky 2, 22 18 bytes

Saved 4 bytes through ovs's optimization.

f=x=>x<1orx*f(x-1) 

When x<1, returns 1 (Due to x<1 being truthy), Otherwise returns x*f(x-1), recursively getting the factorial/

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Haskell, 17 bytes

f n=product[1..n] 

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• Thanks to 79037662 for suggesting it!

18 bytes

f 0=1 f x=x*f(x-1) 

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Or 19 bytes using fold.

f n=foldr(*)1[2..n] 

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Regex 🐇 (RME / PCRE2 _^v10.35+), 12 bytes

^((?*x+)x)*$ 

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Try it on replit.com! - RegexMathEngine, in ECMAScript+(?*) mode

Takes its input in unary, as a string of x characters whose length represents the number. Returns its output as the number of ways the regex can match. (The rabbit emoji indicates this output method. It can yield outputs bigger than the input, and is really good at multiplying.)

^ # tail = N = input number ( (?*x+) # Assert tail > 0; multiply the number of possible matches by tail x # tail -= 1 )* # Iterate the above as many times as possible, minimum zero $ # Assert tail == 0, so that the loop will have iterated N times 

This solution uses (?*...) non-atomic lookahead. It (and any super-exponential function) is likely impossible to implement without some kind of non-atomic lookaround (which would be necessary for compatibility with other regex engines, e.g. Perl).

The problem is, without molecular lookahead, it's necessary to actually advance the cursor (subtract a value from \$tail\$) to try different possibilities in a way that scales with \$n\$. Without using molecular lookaround or advancing the cursor, the number of possibilities can only be multiplied by a constant, e.g. ()?()?()? or (|){3} to multiply them by \$2^3\$, or (||){9} to multiply them by \$3^9\$.

For example, without molecular lookahead, \$2^n\$ can be implemented as ^(x|x)*$ or ^(x+)*, \$3^n\$ as ^(x(||))*$ or ^((x+)*)+, and \$17^n\$ as ^(x((|){4}|))*$ or ^(((((x+)*)+)+)+)+. (The former method can be used for any \$k^n\$, and the latter for \${(2^k+1)}^n\$.) Going off the rails a bit, there are also options like ^(((((x*)*)*)*)*)* for \$\lceil{{80\over 17}154^n}\rceil+1\$.

But for a problem like Factorial, advancing the cursor by more than \$1\$ character per iteration wouldn't leave room for subsequent iterations to have access to the values of \$tail\$ they need.

Note: I accidentally posted this on the wrong Factorial challenge on 2022-07-25. As the amount of time it takes is proportional to the result, it can't even calculate \$12!\$ in under a minute, so that is not the correct place for it. I have deleted it from there and reposted it here.

Prolog (SWI), 28 bytes

N+X:-N>0,N-1+Y,X is Y*N;X=1. 

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Raku, 11 bytes

{[*] 1..$_} 

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{ } : anonymous code block [ ] : reduction metaoperator * : multiplication 1..$_ : range from 1..input 

TypeScript Type System, 82 bytes

type X<A,B=A>=A extends`1${infer R}`?B extends`1${infer O}`?`${X<R>}${X<A,O>}`:B:1 

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Quite similar to, but independently derived from noodle man's answer. I also stole their test harness.

This is basically the same as the JavaScript code f = (a, b = a) => a ? b ? f(a, b - 1) + f(a-1) : 0 : 1. The idea here is that we have two accumulators, a and b, where b starts at the value of a. We repeatedly decrement b and add f(a-1) to the total, which results in the factorial of a.

Ly, 9 8 bytes

^{-1 thanks to cnamejj}

R11[*f]p 

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Ly, for some reason, doesn't have &* (product) like it does &+ (sum). I guess I forgot about it 3 years ago when I made this terrible language.

Python 3.8, ²³ 21 bytes

Saved 2 bytes thanks to Bubbler!!!

import math math.perm 

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tinylisp, 34 bytes

(load library (q((n)(product(1to n 

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Explanation

Using the library functions product and 1to:

(q Quote the following list, which can then be treated as a lambda function ((n) that takes a single argument n: (product Multiply together (if the list is empty, returns 1) (1to n)))) all numbers from 1 up to and including n 

Zephyr, 72 bytes

input n as Integer set f to 1 for i from 1to n set f to f*i next print f 

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Same algorithm as my QBasic answer, just in a more-verbose syntax: If n is zero, the for loop does nothing and 1 is output. Otherwise, the for loop runs over i from 1 up to and including the input number, multiplying the result by each i.

Ruby, 23 19 bytes

->n{Math.gamma n+1} 

-4 bytes using gamma function (Dingus).

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Io, 20 bytes

method(\,\factorial) 

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Python 2, 38 bytes

i=n=1;exec"n*=i;i+=1;"*input();print n 

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K (ngn/k), 6 bytes

Solution:

*/1+!: 

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Explanation:

*/1+!: / the solution !: / range 0..N 1+ / add 1 (vectorised) */ / product 

Extra:

• Also */-!-: for the same byte count.

Assembly (MIPS, SPIM), 108 bytes, 6*10 = 60 assembled bytes

main:li $v0,5 syscall li $a0,1 beqz $v0,e f:mul $a0,$a0,$v0 sub $v0,$v0,1 ble $v0,0,e b f e:li $v0,1 syscall 

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Explanation

main: li $v0, 5 # set syscall code 5 syscall # Read an integer into v0 li $a0, 1 # register a0 = 1 beqz $v0, end # Handle $v0 = 0 case fact: # Main procedure: mul $a0, $a0, $v0 # a0 = a0 * v0 sub $v0, $v0, 1 # v0 = v0 - 1 ble $v0, 0, end # If v0 <= 0, jump to end b fact # Jump back to the start of the procedure end: # After-process: li $v0, 1 # Set sycall code 1 syscall # Output the number stored in a0 

Pepe, 57 bytes

3 bytes have been decreased from my Pepe factorial program.

rrEEReREEEEErEeREeEreEREErEEEEErEEEeeReererRrEEEEEEeEreEE 

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Mornington Crescent, 3788 bytes

109 lines/ops

Take Northern Line to Embankment Take Northern Line to Embankment Take District Line to Parsons Green Take District Line to Ravenscourt Park Take District Line to Embankment Take District Line to Embankment Take Northern Line to Euston Take Victoria Line to Seven Sisters Take Victoria Line to Victoria Take Victoria Line to Victoria Take District Line to Turnham Green Take District Line to Victoria Take District Line to Victoria Take Victoria Line to Seven Sisters Take Victoria Line to Victoria Take Victoria Line to Victoria Take District Line to Turnham Green Take District Line to Notting Hill Gate Take District Line to Notting Hill Gate Take District Line to Embankment Take District Line to Embankment Take District Line to Stamford Brook Take District Line to Embankment Take Northern Line to Goodge Street Take Northern Line to Charing Cross Take Northern Line to Charing Cross Take Northern Line to Tottenham Court Road Take Northern Line to Tottenham Court Road Take Northern Line to Moorgate Take Northern Line to Moorgate Take Metropolitan Line to Preston Road Take Metropolitan Line to Moorgate Take Northern Line to Euston Take Victoria Line to Seven Sisters Take Victoria Line to Euston Take Victoria Line to Euston Take Northern Line to Moorgate Take Northern Line to Moorgate Take Metropolitan Line to Preston Road Take Metropolitan Line to Moorgate Take Northern Line to Moorgate Take Northern Line to Embankment Take Northern Line to Embankment Take Northern Line to Bank Take District Line to Hammersmith Take District Line to West Kensington Take District Line to Hammersmith Take District Line to South Kensington Take District Line to South Kensington Take Piccadilly Line to Bounds Green Take Piccadilly Line to South Kensington Take District Line to Ravenscourt Park Take District Line to Bank Take District Line to Hammersmith Take District Line to Ravenscourt Park Take District Line to Hammersmith Take District Line to South Kensington Take District Line to South Kensington Take Piccadilly Line to Bounds Green Take Piccadilly Line to South Kensington Take Piccadilly Line to South Kensington Take District Line to Ravenscourt Park Take District Line to Temple Take District Line to West Kensington Take District Line to Bank Take District Line to Hammersmith Take District Line to West Kensington Take District Line to Hammersmith Take Piccadilly Line to Eastcote Take Piccadilly Line to Eastcote Take Metropolitan Line to Chalfont & Latimer Take Metropolitan Line to Eastcote Take Piccadilly Line to Ealing Common Take District Line to Ravenscourt Park Take District Line to Bank Take District Line to Hammersmith Take District Line to Ravenscourt Park Take District Line to Hammersmith Take Piccadilly Line to Eastcote Take Piccadilly Line to Eastcote Take Metropolitan Line to Chalfont & Latimer Take Metropolitan Line to Eastcote Take Metropolitan Line to Eastcote Take Piccadilly Line to Ealing Common Take District Line to Ealing Common Take District Line to Bank Take District Line to Hammersmith Take District Line to West Kensington Take District Line to Stamford Brook Take District Line to Bank Take District Line to Hammersmith Take District Line to Stamford Brook Take District Line to Hammersmith Take District Line to Upminster Take District Line to Ravenscourt Park Take District Line to Upminster Take District Line to Bank Take District Line to Hammersmith Take District Line to Ravenscourt Park Take District Line to Hammersmith Take District Line to Embankment Take District Line to Embankment Take Northern Line to Angel Take Northern Line to Embankment Take Northern Line to Embankment Take District Line to West Kensington Take District Line to Embankment Take Northern Line to Embankment Take Northern Line to Mornington Crescent 

Commented version for some explanations:

Take Northern Line to Embankment Take Northern Line to Embankment Take District Line to Parsons Green Take District Line to Ravenscourt Park # Save Input in Ravenscourt Take District Line to Embankment Take District Line to Embankment # Create -1 Take Northern Line to Euston Take Victoria Line to Seven Sisters Take Victoria Line to Victoria Take Victoria Line to Victoria Take District Line to Turnham Green Take District Line to Victoria Take District Line to Victoria Take Victoria Line to Seven Sisters Take Victoria Line to Victoria Take Victoria Line to Victoria Take District Line to Turnham Green Take District Line to Notting Hill Gate Take District Line to Notting Hill Gate Take District Line to Embankment Take District Line to Embankment Take District Line to Stamford Brook # Save -1 in Stamford Brook Take District Line to Embankment # Create 1 Take Northern Line to Goodge Street Take Northern Line to Charing Cross Take Northern Line to Charing Cross Take Northern Line to Tottenham Court Road Take Northern Line to Tottenham Court Road Take Northern Line to Moorgate Take Northern Line to Moorgate Take Metropolitan Line to Preston Road Take Metropolitan Line to Moorgate Take Northern Line to Euston Take Victoria Line to Seven Sisters Take Victoria Line to Euston Take Victoria Line to Euston Take Northern Line to Moorgate Take Northern Line to Moorgate Take Metropolitan Line to Preston Road Take Metropolitan Line to Moorgate Take Northern Line to Moorgate Take Northern Line to Embankment Take Northern Line to Embankment Take Northern Line to Bank Take District Line to Hammersmith Take District Line to West Kensington # Save 1 in West Kensington # Save 1 as max value at Bounds Green, so we will later take the largest number between the input and 1 (to handle 0 as an input) Take District Line to Hammersmith Take District Line to South Kensington Take District Line to South Kensington Take Piccadilly Line to Bounds Green # Save 1 as max Take Piccadilly Line to South Kensington Take District Line to Ravenscourt Park # Get input Take District Line to Bank Take District Line to Hammersmith Take District Line to Ravenscourt Park Take District Line to Hammersmith Take District Line to South Kensington Take District Line to South Kensington Take Piccadilly Line to Bounds Green Take Piccadilly Line to South Kensington Take Piccadilly Line to South Kensington Take District Line to Ravenscourt Park # If input is 0 -> now it is 1 Take District Line to Temple # Save in jumpstack # Take Current Result (West Kensington) as first argument to Chalfont & Latimer Take District Line to West Kensington Take District Line to Bank Take District Line to Hammersmith Take District Line to West Kensington Take District Line to Hammersmith Take Piccadilly Line to Eastcote Take Piccadilly Line to Eastcote Take Metropolitan Line to Chalfont & Latimer Take Metropolitan Line to Eastcote Take Piccadilly Line to Ealing Common # Take Current Value (Ravenscourt Park) as second argument to Chalfont & Latimer Take District Line to Ravenscourt Park Take District Line to Bank Take District Line to Hammersmith Take District Line to Ravenscourt Park Take District Line to Hammersmith Take Piccadilly Line to Eastcote Take Piccadilly Line to Eastcote Take Metropolitan Line to Chalfont & Latimer Take Metropolitan Line to Eastcote Take Metropolitan Line to Eastcote Take Piccadilly Line to Ealing Common Take District Line to Ealing Common # Save the new result n*(n-1) as the current result at West Kensington Take District Line to Bank Take District Line to Hammersmith Take District Line to West Kensington # Put -1 (Stamford Brook) as the first argument of the addition in Upminster Take District Line to Stamford Brook Take District Line to Bank Take District Line to Hammersmith Take District Line to Stamford Brook Take District Line to Hammersmith Take District Line to Upminster # Put The current value (Ravenscourt Park) as the second argument of the addition in Upminster -> [decrement], save it in the current value Take District Line to Ravenscourt Park Take District Line to Upminster Take District Line to Bank Take District Line to Hammersmith Take District Line to Ravenscourt Park Take District Line to Hammersmith Take District Line to Embankment Take District Line to Embankment Take Northern Line to Angel # Check if we reached 0 as current value, if it equals 0, break the loop and continue here: Take Northern Line to Embankment Take Northern Line to Embankment Take District Line to West Kensington # Get the final result Take District Line to Embankment Take Northern Line to Embankment Take Northern Line to Mornington Crescent # Print and exit 

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GolfScript, 9 bytes

1\~,{)*}/ 

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1\ # Puts 1 under the input, this will be the acumulator ~, # Makes an array with numbers from 0 to (n-1) {)*} # This block goes to the top of the stack without being executed, when executed it increments and multiplies, this avoids multiplying by 0 and also multiplies by n / # Executes the previous block for each number in the array 

Whispers v3, 25 bytes

> Input >> 1! >> Output 2 

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Squeezed pseudo code:

>> Output ((Input)!) 

Explanation:

As always in Whispers, we run the last line first:

>> Output 2 

This line outputs the result from line 2:

>> 1! 

Use the result from line 1 to calculate the factorial (line 1)!

> Input 

Takes the first line of the input.

So we get the squeezed pseudo code:

>> Output ((Input)!) 

PowerShell Core, 37 32 bytes

param($a)1..($a+!$a)-join'*'|iex 

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Or recursive:

PowerShell Core, 37 36 bytes

filter f{if($_){$_*(--$_|f)}else{1}} 

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All bytes reductions thanks to mazzy :)

Vyxal, 1 byte

¡ 

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Built-in factorial.

No built-in, 2 bytes

ɾΠ 

Explanation:

 # Implicit input ɾ # Range [1, N] Π # Reduce by multiplication # Implicit output 

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Python 3, 61 50 48 bytes

a=1 for i in range(int(input())):a*=i+1 print(a) 

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Thanks to Bubbler for shortening the code by 11 bytes. Another thanks to Jo King♦ for shortening the code by 2 bytes.

Rockstar, 70 66 62 61 60 55 bytes

listen to N F's1 while N let F be*N-0 let N be-1 say F 

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Quipu, 41 bytes

1&1&1&0& []--[][] **2&0&/\ 1&>=>> >>\/ 1& 

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This was written for the Learn you a Lang event (just like Aaron Miller's answer). This turned out surprisingly clean, with only 4 threads and no spaces.

Explanation

Quipu uses multiple threads (these are each column of two characters). The Scala interpreter I'm using here doesn't need spaces between threads, though the other interpreter on Esoteric IDE does need the separation, and actually supports the BigInt needed for factorials above the max integer value.

Anyway, thread zero is where we store the actual factorial value. All threads have the initial value of 0.

1& Push 1 [] Get the value of thread 1 (where the input number will be stored) ** Multiply it by the current thread 0 value 1& Push 1 >> Jump to thread one if the current value is greater than zero 1& Otherwise push one to initialise the value (this happens on the first iteration) 

After jumping, the current thread value is set to the value being checked, in this case, current value multiplied by thread one. When the current value is zero and the input has not yet been retrieved (and is also zero), we don't jump, setting the current value to the last knot (the 1).

Either way we move onto the next thread. Thread one is where we get the input and decrement it over each loop.

 1& Push one -- Subtract one from the current value 2& Push two >= Jump to thread two if the value is greater than or equal to zero \/ Otherwise push the input 

Similar to thread zero, we initialise this value to the input if it was initially zero. Otherwise, we decrement the value. Next is thread two.

 1& Push 1 [] Get the value of thread one 0& Push zero >> Jump back to thread zero if the value is still greater than zero 

This loops back over the first two threads until the input has reached zero, multiplying the value of thread zero by each element in the range of 1 to the input. Once we're done, we finally execute thread three and terminate.

 0& Push zero [] Get the value of thread zero /\ And print 

Knight, 25 bytes

;=x+=y 1P;W=x-x 1=y*x yOy 

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Ungolfed:

; = x + x = sum of: = y 1 y = 1 (passes through 1) and PROMPT a line from stdin (coerced to number) ; WHILE = x - x 1 while (x = x - 1) is nonzero: = y * x y y = x * y OUTPUT y print y 

In Knight, coercion depends on the type of the first argument. So 1+"5" is 6 while "5"+1 is "51".

JavaScript, 19 bytes

f=n=>n?f(n-1n)*n:1n 

2 bytes longer than the other JS answers, but can safely calculate as high as 11190! instead of 18!, with anything higher exceeding the call stack size (tested on Node.js 18.6.0). the result has 40450 digits.

update: running with --stack-size=65536 allows me to calculate up to 95200!, resulting in 432625 digits. Trying to calculate any higher caused segmentation faults, no matter what I set the stack size to.

Brachylog, 1 byte

ḟ 

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Also works with a fixed output and an unknown input, with decent performance.

No built-in, 3 bytes

⟦b× 

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