1. Objectives The student will be able to: 1. find the prime factorization of a number. 2. find the greatest common factor (GCF) for a set of monomials. SOL: A.2c Designed by Skip Tyler, Varina High School

2. A prime number is a number that can only be divided by only one and itself. A composite number is a number greater than one that is not prime. Prime or composite? 37 prime 51 composite

3. Prime or Composite? 89 1.Prime 2.Composite 3.Both 4.Neither

4. 1) Find the prime factorization of 84. 84=4 21 =2 2 3 7 2) Find the prime factorization of -210. -210=-1 210 =-1 30 7 = -1 6 5 7 =-1 2 3 5 7

5. What is the prime factorization of 48? 1. 3  16 2. 3  4  4 3. 2  2  3  4 4. 2  2  2  2  3

6. 3) Find the prime factorization of 45a 2 b 3 (Factor the monomial completely) 45a 2 b 3 = 9 5 a a b b b =3 3 5 a a b b b = 3 2 5 a a b b b Write the variables without exponents.

7. What is the prime factorization of…. (Factor the monomial completely) 12g 2 h 4

8. What is the prime factorization of…. (Factor the monomial completely) -38rp 2 t 2

9. What is the prime factorization of…. (Factor the monomial completely) -17x 3 y 2 z

10. The Greatest Common Factor (GCF) of 2 or more numbers is the largest number that can divide into all of the numbers. 4) Find the GCF of 42 and 60. Write the prime factorization of each number.

11. 4) Find the GCF of 42 and 60. What prime factors do the numbers have in common? Multiply those numbers. The GCF is 2 3 = 6 6 is the largest number that can go into 42 and 60! 42 =2 3 7 60=2 2 3 5

12. Another Method Find the GCF of 42 and 60.

13. What is the GCF of 48 and 64? 1.2 2.4 3.8 4.16

14. What is the GCF of 24 and 56? 1.8 2.6 3.3 4.4

15. 5) Find the GCF of 40a 2 b and 48ab 4. 40a 2 b = 2 2 2 5 a a b 48ab 4 = 2 2 2 2 3 a b b b b What do they have in common? Multiply the factors together. GCF = 8ab

16. What is the GCF of

19. Party Favors Balloons come in packages of 18 and party hats come in packages of 8. You want to have the same number of balloons and hats. What is the fewest packages of each you need to buy so you have no hats or balloons left over?