Prime factorization algorithms are algorithms that have been devised for determining the prime factors of a given number (a process called prime factorization).

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and complexity. It is very difficult to build a general-purpose algorithm for this computationally "hard" problem, so any additional information that is known about the number in question or its factors can often be used to save a large amount of time. The simplest method of finding factors is so-called "direct search factorization" (a.k.a. trial division). In this method, all possible factors are systematically tested using trial division to see if they actually divide the given number. It is practical only for very small numbers.

Brent's factorization method | continued fraction factorization algorithm | direct search factorization | Dixon's factorization method | elliptic curve factorization method | Euler's factorization method | excludent factorization method | Fermat's factorization method | Legendre's factorization method | number field sieve | Pollard p-1 factorization method | Pollard ρ factorization method | prime factorization | prime number | quadratic sieve | quiteprime | trial division | veryprime | Williams p+1 factorization method

college level