Factorials grow very quickly and results exceed the limits of computer floating point arithmetic already for 200! It is therefore more convenient to work with the logarithms of factorials. $log(n!) = log(1) + log(2) + log(3) + \ldots + log(n)$ would do the work but it is too slow to iterate the various log computations. There are alternatives to this naive approach. The first is to express the factorial in terms of the gamma function: $n! = \Gamma(n+1)$. The second is to use Stirling's approximation: $log \Gamma(n) \approx (n – 1/2) \log(n) – n + (1/2) log(2 \pi) + 1/(12 n) – 1/(360 n^3) + 1/(1260 n^5) – \ldots$ which uses Bernoulli's numbers.