1) The greatest common factor (GCF) is the largest factor that is common to all terms of a polynomial expression. 2) To find the GCF, identify the common monomial factors in each term and take their product. 3) Once the GCF is identified, it is factored out of the original polynomial expression. The remaining terms are grouped together in parentheses.

1. Factoring by using the
Greatest Common Factor (GCF)
Lesson 2.5
Page 77

2. Recall finding the Prime Factorization of a number
1.
2.
20 5 4= × 5 2 2= × ×
2
150x 15 10 x x= × × ×
5 3 5 2 x x= × × × × × 2 3 5 5 x x= × × × × ×
2 2 5= × ×

3. Finding the GCF
The GCF is the product of the common
factors in each term of the polynomial.
4 2
Factor the GCF out of 14 21 .x x−
4
14 2 7 xxx xx= × × × × ×
2
21 3 7 xx x= × × ×

4. Then use the distributive property
to factor the GCF out of the
polynomial.
2
7GCF o xr 7x x= × ×
2 2 24
7 (1 3)14 22x x xx = −−
When you factor the GCF out of a polynomial,
what remains in each term goes in parentheses.

5. Find the GCF of the following:
1.
2.
3.
3
15 , 20xx 5x
3 2 2 2
8 , 12abc a b c
2
4abc
2 4 3
6 , 15x y x yz
2
3x y

6. Factor out the greatest common
monomial factor.
The GCF is 8.
8 8x y−
8( )x y−

7. Factor out the greatest common
monomial factor.
4 2
14 35a a+
2
The GCF is 7 .a
2 2
7 (2 5)a a +

8. Try the following.
3
5 4
2
1. 4 6
2. 44 33
3. 6 14
4. 15 5
r rs
m mn
y y
a b ab
+
−
−
+

9. Answers:
1. 2 (2 3 )r s+
2
2. 11 (4 3 )m m n−
4
3. 2 (3 7)y y −
4. 5 (3 1)ab a +

10. Homework Assignment:
Page 79 # 13 – 21 all
Page 80 # 10 – 18 all