do you love factoring numbers? me too. whether you're helping your little cousin with her algebra homework or trying to crack an rsa cryptosystem, there's nothing quite like the thrill of taking a big number and writing it as a product of smaller numbers. in this talk we present a brief historical overview of some primality tests and factorization methods; we will also develop in more detail the quadratic sieve method developed by pomerance in the 1980's, which for many years held the record for fastest implementation of a factorization algorithm. we leave the converse question of how to create a large number from several smaller numbers as an exercise to the interested listener.