Legendre's Formula

Gre Glossary

A formula giving the exponent of a prime p in n! as the sum floor(n/p) + floor(n/p²) + floor(n/p³) + …, i.e. ∑ₖ floor(n/pᵏ). It is the fast way to count trailing zeros of a factorial or the power of a prime dividing it.

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