Download Find the greatest common factor (GCF).

Warm Up
Write the prime factorization of each
number.
1. 20
22 · 5
2. 100
22 · 52
3. 30
2·3·5
4. 128
27
5. 70
2·5·7
Learn to find the greatest common factor
of two or more whole numbers.
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Vocabulary
greatest common factor (GCF)
The greatest common factor (GCF) of two or
more whole numbers is the greatest whole
number that divides evenly into each number.
One way to find the GCF of two or more numbers
is to list all the factors of each number. The GCF
is the greatest factor that appears in all the lists.
Using a List to Find the GCF
Find the greatest common factor (GCF).
12, 36, 54
12: 1, 2, 3, 4, 6, 12
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
54: 1, 2, 3, 6, 9, 18, 27, 54
The GCF is 6.
List all of the factors
of each number.
Circle the greatest
factor that is in all
the lists.
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Try This: Example 1
Find the greatest common factor (GCF).
14, 28, 63
14: 1, 2, 7, 14
28: 1, 2, 4, 7, 14, 28
63: 1, 3, 7, 9, 21, 63
The GCF is 7.
List all of the factors of
each number.
Circle the greatest
factor that is in all
the lists.
Example : Using Prime Factorization to Find the GCF
Find the greatest common factor (GCF).
A. 40, 56
40 = 2 · 2 · 2 · 5 Write the prime factorization of
each number and circle the
56 = 2 · 2 · 2 · 7 common factors.
2·2·2=8
The GFC is 8.
Multiply the common prime
factors.
Example : Using Prime Factorization to Find the GCF
Find the greatest common factor (GCF).
B. 252, 180, 96, 60
Write the prime factorization
252 = 2 · 2 · 3 · 3 · 7 of each number and circle
180 = 2 · 2 · 3 · 3 · 5 the common prime factors.
96 = 2 · 2 · 2 · 2 · 2 · 3
60 = 2 · 2 · 3 · 5
2 · 2 · 3 = 12
The GCF is 12.
Multiply the common prime
factors.
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Try This: Example
Find the greatest common factor (GCF).
A. 72, 84
72 = 2 · 2 · 2 · 9 Write the prime factorization
of each number and circle
84 = 2 · 2 · 7 · 3
the common factors.
2·2=4
Multiply the common prime
factors.
The GCF is 4.
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Try This: Example
Find the greatest common factor (GCF).
B. 360, 250, 170, 40
360 = 2 · 2 · 2 · 9 · 5 Write the prime factorization
of each number and circle
250 = 2 · 5 · 5 · 5
the common prime factors.
170 = 2 · 5 · 17
40 = 2 · 2 · 2 · 5
2 · 5 = 10
The GCF is 10.
Multiply the common prime
factors.
Example : Problem Solving
You have 120 red beads, 100 white
beads, and 45 blue beads. You want to
use all the beads to make bracelets that
have red, white, and blue beads on each.
What is the greatest number of
matching bracelets you can make?
Example Continued
• There are 120 red beads, 100 white beads,
and 45 blue beads.
• Each bracelet must have the same
number of red, white, and blue beads.
The answer will be the GCF of 120, 100, and 45.
Example Continued
You can list the prime factors of 120, 100,
and 45 to find the GFC.
120 = 2 · 2 · 2 · 3 · 5
100 = 2 · 2 · 5 · 5
45 = 3 · 3 · 5
The GFC of 120, 100, and 45 is 5.
You can make 5 bracelets.
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Try This: Example
Nathan has made fishing flies that he
plans to give away as gift sets. He has
24 wet flies and 18 dry flies. Using all of
the flies, how many sets can he make?
List the important information:
• There are 24 wet flies and 18 dry flies.
The answer will be the GCF of 24 and 18.
Example Continued
You can list the prime factors of 24 and 18
to find the GCF.
24 = 2 · 2 · 2 · 3
18 = 2 · 3 · 3
2·3=6
Multiply the prime factors
that are common to both
24 and 18.
You can make 6 sets of flies.
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Lesson Quiz: Part 1
Find the greatest common factor (GCF).
1. 28, 40
4
2. 24, 56
8
3. 54, 99
9
4. 20, 35, 70 5
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Lesson Quiz: Part 2
5. The math clubs from 3 schools agreed to a
competition. Members from each club must be
divided into teams, and teams from all clubs
must be equally sized. What is the greatest
number of members that can be on a team if
Georgia has 16 members, William has 24
members, and Fulton has 72 members?
8