A factorial, denoted as n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1. Factorials grow extremely rapidly - 20! already has 19 digits, and 100! has 158 digits.

0! = 1 by mathematical convention. This definition makes many mathematical formulas work correctly, particularly in combinatorics where the number of ways to arrange zero objects (an empty set) is one way - by doing nothing. It also maintains the recursive property that n! = n × (n-1)!, so 1! = 1 × 0! requires 0! = 1.

Trailing zeros in n! come from factors of 10, which require pairs of 2 and 5. Since there are always more factors of 2 than 5, count the factors of 5. The formula is: floor(n/5) + floor(n/25) + floor(n/125) + ... For example, 100! has floor(100/5) + floor(100/25) + floor(100/125) = 20 + 4 + 0 = 24 trailing zeros.