Prime factorization means to break a number down into its smallest factors or in other words its prime number factors. You can do this by repeated dividing factors until you get to prime numbers. For instance 105 can be broken down into 21 x 5. 21 can be broken down into 7 x 3. Now you have all the prime factors which are 3 x 7 x 5 which should equal 105 if multiplied together.