You have it exactly backwards. 100 factorial cannot be represented by a float (or double, or long double) 100! = 9332621544394415268169923885626670049071596826

You have it exactly backwards. 100 factorial cannot be represented by a float (or double, or long double) 100! = 9332621544394415268169923885626670049071596826438162146859296389521759\ 9993229915608941463976156518286253697920827223758251185210916864000000\ 000000000000000000 This is 2^(524.765) > 2^32 or 2^64 or 2^80 or 2^128 Note that "floating point" is commonly used to refer to 32-bit or 64-bit or 80-bit representations. Floats are for games (with caveats), and possibly engineering, while purer math needs arbitrary-precision representations that are too slow for games and many simulations.