1. Factoring using GCF Tuesday August 14th 2012

2. GCF
Greatest
Common
Factor

3. What is a factor? Lets look at the factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36

4. What is a factor?
You list the factors of 12:
1, 2, 3, 4, 6, 12

5. What are the common factors of 12 and 36?
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
12: 1, 2, 3, 4, 6, 12
Of these factors, which is the greatest or the GCF?

6. Example 1 Find the GCF of 30 and 42
common factor is a whole number that is a factor of each number.
greatest common factor (GCF) is the greatest of their common factors.
Example 1
Find the GCF of 30 and 42

7. Caution: Do not confuse GCF with LCM.
A multiple of a whole number is the product of the number and any nonzero whole number. A common multiple of two or more whole numbers is a multiple of each number. The least common multiple (LCM) of two or more whole numbers is the least of their common multiples.
Example 2
Find the LCM of 10 and 15

8. Now lets apply GCF to polynomials:
Example 3
Given the polynomial 2x + 10, determine the GCF.

9. Now lets apply GCF to polynomials:
Given the polynomial 6x-2y, determine the GCF.

10. Now lets apply GCF to polynomials:
Given the polynomial 2x2 + 6x, determine the GCF.

11. Now lets apply GCF to polynomials:
Given the polynomial Find the GCF of 40a2b and 48ab4, determine the GCF.

12. Determine the GCF for each of the following:

13. Now let’s factor
Example 4
Factor 7x+14 using the GCF

14. Factor 9x - 33 using the GCF

15. Factor x2 + 8x using the GCF

16. Example 5
Factor using GCF

17. Factor these on your own looking for a GCF.6. 7. 8.