Do all factorials end in 0

Not all factorials end in zero—specifically, factorials from 1! through 4! (equaling 1, 2, 6, and 24 respectively) do not end in zero. Starting with 5!, every factorial thereafter ends in at least one zero, and the number of trailing zeros increases as the factorial grows because trailing zeros result from pairs of factors 2 and 5, which combine to create factors of 10.

The pattern emerges because 5! = 120 (containing one pair of 2 and 5), and every subsequent factorial includes all previous factors plus new ones. Since even numbers contribute abundant factors of 2, the limiting factor is how many 5s appear in the multiplication sequence. Each multiple of 5 adds at least one trailing zero, multiples of 25 add an extra zero, and so on. This means 10! has 2 trailing zeros, 25! has 6 trailing zeros, and 100! has 24 trailing zeros. Understanding this pattern is valuable in number theory, algorithm design for large number calculations, and predicting computational behavior when working with factorial-based formulas in probability and combinatorics.