Download Factoring GCF

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.
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 21 and 35.
Step 1: List factors for both numbers. 21: 1,3,7,21
Step 2: Identify the highest common
factor.
7 is the GCF of 21 and 35.
35: 1,5,7,35
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
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.
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( ___
5a + ___
3 )
25a 2
5a
15a
5a
Check your answer by distributing.
2) Factor
2
18x
-
3
12x .
Find the GCF
6x2
Divide each term by the GCF
18x2 - 12x3 = 6x2( ___
___ )
3 - 2x
18 x 2
6x2
12 x 3
6 x2
Check your answer by
distributing.
3) Factor 28a2b + 56abc2.
GCF = 28ab
Divide each term by the GCF
28a2b + 56abc2 = 28ab ( ___
2c2 )
a + ___
2
28a b
28ab
56abc 2
28ab
Check your answer by distributing.
28ab(a + 2c2)
Factor 20x2 - 24xy
1.
2.
3.
4.
x(20 – 24y)
2x(10x – 12y)
4(5x2 – 6xy)
4x(5x – 6y)
5) Factor 28a2 + 21b - 35b2c2
GCF = 7
Divide each term by the GCF
28a2 + 21b - 35b2c2 = 7 ( ___
4a2 + ___
3b - ____
5b2c2 )
28a 2
7
21b
7
35b 2 c 2
7
Check your answer by distributing.
7(4a2 + 3b – 5b2c2)
Factor 16xy2 - 24y2z +
2
40y
1.
2.
3.
4.
2y2(8x – 12z + 20)
4y2(4x – 6z + 10)
8y2(2x - 3z + 5)
8xy2z(2 – 3 + 5)
Practice Worksheet