The Greatest Common Factor And Factoring By Grouping Worksheet With Answer Key - Section 6.1 Page 2
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4Section 6.1 The Greatest Common Factor and Factoring by Grouping
(Solution 2)
Step 1: Prime Factorization (ignore signs)
6
∙ 3
2
∙
Step 2: List all factors that are common to all terms
Common factors to all are
2
and
x
Step 3: Choose the smallest power
The smallest power for 2 is 1
The smallest power for x is 2
So, the GCF is 2 ∙
Factoring out GCF
6
2
6
2
3,
2
2
(Solution 3)
Step 1: Prime Factorization (ignore signs)
7
21
3 ∙
35
5 ∙
Step 2: List all factors that are common to all terms
Common factors to all are
7
and x.
Step 3: Choose the smallest power
The smallest power for 7 is 1
The smallest power for x is 2
So, the GCF is 7 ∙
Factoring out GCF
7
21
35
7
21
35
,
,
7
7
7
(Solution 4)
Step 1: Prime Factorization (ignore signs)
27
3 ∙ 3 ∙ 3
3
29
29 because 29 is prime number
Step 2: List all factors that are common to all terms
There is no common factor.
Therefore, 27
29 cannot be factored.
or 27
29 is prime.
Cheon-Sig Lee
Page 2
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