Squarefree factorization is a first step in many factoring algorithms. It factors nonsquarefree polynomials in terms of squarefree factors that are relatively prime. It can separate factors of different multiplicities, but not factors with the same multiplicity. One way to find a squarefree factorization is to compute polynomial greatest common denominators iteratively. The squarefree part (i.e., product of all distinct monic irreducible factors) of a monic nonconstant polynomial p in a field of characteristic zero is p/GCD(p, p'), where p' is the derivative of p.

factorization | prime factorization