KnowraPrime factorizationLinked fromLinked fromThe 40 pages that link to Prime factorization, each with the reason it gives.All 40Broader topic 3Related 29Narrower topic 8Euclid's lemmaNarrower topic: Applying the lemma repeatedly establishes that this representation is unique up to order.Divisor functionNarrower topic: Its exponents determine the formulas for counting and summing divisors.p-adic valuationNarrower topic: The valuation extracts one prime's exponent from this factorization.Perfect numberNarrower topic: The structure of a perfect number’s divisors follows directly from its prime factors.Euclid–Euler theoremNarrower topic: The theorem's converse rests on factoring the number after separating its largest power of two.Legendre's formulaNarrower topic: The formula computes one prime's exponent in this decomposition.abc conjectureNarrower topic: The radical is obtained by retaining each prime factor only once.Highly composite numberNarrower topic: The exponents in this expression determine how many divisors the integer has.