# 046. Use GAMMA to compute factorials topic: {ref}`math-intrinsic-functions` Why does Fortran not have a factorial function? It does, as for positive whole values of $n$, the [gamma function](https://en.wikipedia.org/wiki/Gamma_function) simplifies to the factorial function for $n-1$. That is, ``` n! == gamma(n+1) ``` ```{literalinclude} ../../src/factorial.f90 :language: fortran :caption: factorial.f90 | | ₀ |

``` ```{code-block} text :caption: Output[^gfortran-version] factorial of 0 is 1.0000000000000000 or 1.0000000000000000 factorial of 1 is 1.0000000000000000 or 1.0000000000000000 factorial of 5 is 120.00000000000000 or 120.00000000000000 factorial of 11 is 39916800.000000000 or 39916800.000000000 factorial of 170 is 0.72574156153079940E+307 or 0.72574156153079990E+307 1.7976931348623157E+308 ``` [^gfortran-version]: Compiled using `GNU Fortran (Ubuntu 11.3.0-1ubuntu1~22.04) 11.3.0` with no flags Intrinsic function [`gamma`](https://gcc.gnu.org/onlinedocs/gfortran/GAMMA.html) was added in the F2008 standard. We can see that $170!$ is close to the real64 limit. $171!$ [would be](https://www.wolframalpha.com/input?i=171%21) too large. Also used above: * implied `do` loop for computing the array passed to `product` * assumed-size array (`n(*)`) -- the size is "assumed" from the size of the array literal on the right-hand side of the equals sign * `g0` edit descriptor and `*` infinite repeat count -- see Tip 041 ```{note} Thanks to [@urbanjost](https://github.com/urbanjost) [for this tip and code](https://github.com/Beliavsky/FortranTip/issues/19). ``` ---

Why does Fortran not have a factorial function? It does, as for positive whole values of X the Gamma function simplifies to the factorial function for (X-1).
That is,

x! == gamma(x+1)

Thanks to urbanjost for tip! pic.twitter.com/fTAPvhKEpr
— FortranTip (@fortrantip) December 24, 2021