1. Bell Work: Express 90 as a product of factors.

2. Answer: 2 x 3 x 3 x 5

3. Lesson 34: Greatest Common Factor

4. The number 210 has four prime number factors, as shown here. 2 x 3 x 5 x 7 = 210

5. We call factors that are numbers numerical factors. Some expressions have factors that are letters, and some expressions have both numbers and letters as factors.

6. Example: 210xy z = 2  3  5  7  x  y  y  z  z  z 23

7. We call the letter factors literal factors, and we use the words algebraic factor as a general term to describe factors that are either numbers or letter or both numbers and letters.

8. GCF*: (Greatest Common Factor) Of two or more terms is the product of all prime algebraic factors common to every term, each to the highest power that it occurs in all of the terms.

9. The expression 6x y m + 3xy m + 3x y can be written as 2  3  x  x  y  y  m  m + 3  x  y  y  y  m  m + 3  x  x  x  y  y 2 2 23 2 32

10. Now only the first term has 2 as a factor, so 2 is not a part of the GCF. Each term has 3 as a factor at least once, so 3 is a factor of the GCF of all the terms. 3

11. Each term has x as a factor at least once in every term, so x is a factor of the GCF. x

12. In the same way, y is used as a factor at least twice in every term, so the greatest common factor of the three given terms is 3xy The variable m is not included because it is not a factor of the third term of the original expression. 2

13. Practice: Find the Greatest Common Factor of 8z m p – 12z m p. 4 234 2

14. Answer: 4z m p 32

15. Practice: Find the GCF of 4x y z – 8y xz 232 3

16. Answer: 4xy z 2

17. Find the greatest common factor of 16x yp – 4x y p + 2x y p 23322215

18. Answer: 2x yp 2

19. HW: Lesson 34 #1-30 Due Tomorrow