Legendre's Formula

Legendre's formula gives the exponent of a prime p in the prime factorization of a factorial n!, expressing it as the sum over k of the floor of n divided by p to the power k. Equivalently, it can be computed from the sum of the base-p digits of n, subtracted from n and divided by p minus 1. The formula is a basic tool in number theory and combinatorics for determining how many trailing zeros a factorial has in a given base, since the number of trailing zeros in base 10 depends on the exponent of 5 dividing n!. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/