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Greatest Common Factor
What it is and how to find it!
Greatest Common Factor (GCF)
• The greatest common factor is the largest
factor that two numbers share.
• Let’s find the GCF of 12 and 42. First, we
need to make a list of factors for each
number.
12
1 x 12
2x6
3x4
4x3
42
1 x 42
Factors of 12:
2 x 21
3 x 14
1, 2, 3, 4, 6,12
4 x ??
Factors of 42:
5 x ??
1, 2, 3, 6, 7, 14, 21, 6 x 7
7x6
42
Common Factors: 1, 2, 3, 6
Greatest Common Factor: 6
What is the GCF of 18 and 27?
18
1 x 18
2x9
3x6
Factors of 18:
4x?
5x?
1, 3, 9, 27
6x3
1, 2, 3, 6, 9, 18
Factors of 27:
Common Factors:
1, 3, 9
GCF: 9
27
1 x 27
2x?
3x9
4x?
5x?
6x?
7x?
8x?
9x3
What is the GCF of 48 and 60?
48
1 x 48
2 x 24
3 x 16
4 x 12
6x8
60
1 x 60
2 x 30
3 x 20
4 x 15
5 x 12
6 x 10
Factors of 48:
1, 2, 3, 4, 6, 8, 12, 16,
24, 48
Factors of 60:
1, 2, 3, 4, 5, 6, 10, 12,
15, 20, 30, 60
Common Factors: 1, 2, 3, 4, 6, 12
GCF: 12
Using Prime Factorization
•Find the prime factorization of each
number.
•Identify the common factors and
multiply them.
Example: GCF of 27 and 36
27
3x9
3x3
Ans.
3x3x3
•Both prime factorizations
have 3x3 in common.
36
2 x 18
•Therefore, the GCF is 9.
2x9
3x3
Ans. 2x2x3x3
Remember, you can use Our Friend
Venn to organize your factors!
Three numbers
Two numbers (look where the two
circles overlap for GCF!
Factors
of first
number
(not
shared)
Shared
factors
of both
numbers
Factors
of 2nd
number
(not
shared)
Factors of first
number (not
shared)
Shared factors of
1st and 2nd
number
Factors of 2nd
number (not
shared)
Magic triangle! Put factors shared by all
three numbers here! That’s the GCF!
Shared factors of
1st and 3nd number
Shared
factors of 2nd
and 3rd
number
Factors of 3rd
number (not
shared)