Standard practice algorithms for prime factorization of a integer n known to be composite of two primes, p and q, use the modular structure of integers to attempt to do prime factorization. We present a very simple and intuitive algorithm for prime factorization on a simpler premise, that n is the product of two integers and only two integers. Note that p > sqrt(n) WLOG. p = sqrt(n) q = n / p num_runs = 0