KnowraLegendre's formulaLinked fromLinked fromThe 4 pages that link to Legendre's formula, each with the reason it gives.All 4Related 3Compared with 1Prime-counting functionRelated: It provides an exact inclusion-exclusion route to counting primes.p-adic valuationRelated: It computes the valuation of factorials directly from base-p divisibility.Lifting-the-exponent lemmaCompared with: It solves a related valuation problem, but counts prime factors in factorials rather than power differences.Lucas's theoremRelated: It provides a classical route to studying prime divisibility of binomial coefficients.