Fast integer factorization is a problem not yet solved for arbitrary integers. Integer factorization methods are algorithms that find the prime divisors of any positive integer. The goal of this dissertation is to survey integer factorization algorithms and specifically the General Number Field Sieve algorithm. In this work we outlined integer factorization methods. In particular, we consider the General Number Field Sieve (GNFS), the current fastest known algorithm for factorizing integers (Large integers).