Should you fear factoring?  If you accept the premise of the 1992 Robert Redford movie <i>Sneakers</i>, then your life would be in great peril if you were to invent a technique to quickly factor large numbers.  The security of the RSA encryption scheme lies in the fact that currently there is no known factoring procedure that can factor $200+$digit numbers in a reasonable amount of time.  In this talk we will examine several methods of factoring numbers with a focus on the quadratic sieve.  The talk should be accessible to those familiar with the basics of modular arithmetic.