Prime factorization is a way of showing which prime numbers (numbers that can only be divided by one and itself) can go into a number. For instance, the prime factorization of 4 would be 2 x 2. Two can only be divided by one and itself, so it is a prime number, and 2 x 2 = 4. For larger numbers, divide by a prime number until the number that is being divided is a prime number. Each divisor will be used as part of the prime factorization. The final dividend will also be used. Add the dividend, order each divisor from least to greatest, and then you're done. Therefore, the prime factorization of 40 would be 2 x 2 x 2 x 5.