1. Objectives The student will be able to:
Factor using the greatest common factor (GCF).
MM1A2f: Factor expressions by greatest common factor, grouping, trial and error, and special products.

2. Greatest Common Factors (GCF) of Numbers
Greatest Common Factor: The largest number that will divide into 2 or more numbers evenly.
For example; Find GCF for and 35.
Step 1: List factors for both numbers. 21: 1,3,7, : 1,5,7,35
Step 2: Identify the highest common
factor.
7 is the GCF of 21 and 35.

3. Now you try….. Find GCF for the following. 12,18 10,35 8,30 16,24
28,35,49
27,36,63
30,45,60

4. Find GCF of Polynomials
To find the GCF of polynomials, first find the GCF of the coefficients.
Example: 3x2 – 9x GCF of 3 and 9 is 3.
Then, determine what variables the have in common.
3x2 – 9x There is one ‘x’ in both terms.
The GCF of the polynomial is 3x.

5. What is the GCF of 25a2 and 15a? 5a Let’s go one step further…
1) FACTOR 25a2 + 15a.
Find the GCF and divide each term
25a2 + 15a = 5a( ___ + ___ )
Check your answer by distributing. 5a 3

6. 2) Factor 18x2 - 12x3. Find the GCF 6x2 Divide each term by the GCF
18x2 - 12x3 = 6x2( ___ - ___ )
Check your answer by distributing. 3 2x

7. 3) Factor 28a2b + 56abc2. GCF = 28ab Divide each term by the GCF 2c2 a
28a2b + 56abc2 = 28ab ( ___ + ___ )
Check your answer by distributing.
28ab(a + 2c2) a
2c2

8. Factor 20x2 - 24xy
x(20 – 24y)
2x(10x – 12y)
4(5x2 – 6xy)
4x(5x – 6y)

9. Divide each term by the GCF
5) Factor 28a2 + 21b - 35b2c2
GCF = 7
Divide each term by the GCF
28a2 + 21b - 35b2c2 = 7 ( ___ + ___ - ____ )
Check your answer by distributing.
7(4a2 + 3b – 5b2c2)
4a2 3b
5b2c2

10. Factor 16xy2 - 24y2z + 40y2 2y2(8x – 12z + 20) 4y2(4x – 6z + 10)
8xy2z(2 – 3 + 5)

11. Practice Worksheet