Compute n! exactly for large n with big-integer math, and see how many digits it has.
n! is the product of all whole numbers from 1 to n. For example 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition 0! = 1.
Yes. It uses exact big-integer arithmetic, so even 1000! (over 2500 digits) is computed precisely with no scientific-notation rounding.
Counting permutations and combinations, probability, and series expansions in maths and statistics.