1. 1 PRIME FACTORIZATION

2. 2  Every composite number can be expressed as a product of prime numbers. This is called the prime factorization of a number.

3. 3 PRIME FACTORIZATION  To find the prime factorization of a number, you can use a factor tree.

4. 4 FACTOR TREES 36 6 x 6 ^ ^ 2 x 3 ^ 36 = 2 x 2 x 3 x 3 or 2 ² x 3²3²

5. 5 FACTOR TREES 36 3 x 12 ^ ^ 3 x 4 36 = 2 x 2 x 3 x 3 2 x 2 ^ or 2 ² x 3²3²

6. 6 FACTOR TREES 9 3 x 3 ^ 9 = 3 x 3 or 3²3²

7. 7 FACTOR TREES 21 3 x 7 ^ 21 = 3 x 7

8. 8 FACTOR TREES 100 10 x 10 ^ ^ 2 x 5 ^ 100 = 2 x 2 x 5 x 5 or 2 ² x 5²5²

9. 9 PRIME FACTORIZATION  To find the prime factorization of a number, you can use a factor ladder.

10. 10 FACTOR LADDERS 36 18 36 = 2 x 2 x 3 x 3 or 2 ² x 3²3² Begin with the least prime number that is a factor. Repeat until the quotient is prime.  2 2 3 3   9

11. 11 FACTOR LADDERS 60 30 60 = 2 x 2 x 3 x 5 or 2 ² x 3 x 5 Begin with the least prime number that is a factor. Repeat until the quotient is prime.  2 2 3 5   15

12. 12 FACTOR LADDERS 45 15 45 = 3 x 3 x 5 or 3 ² x 5 Begin with the least prime number that is a factor. Repeat until the quotient is prime.  3 3 5 

13. 13 FACTOR LADDERS 125 25 125 = 5 x 5 x 5 or 5³ Begin with the least prime number that is a factor. Repeat until the quotient is prime.  5 5 5 