Learn to find the greatest common factor of two or more whole numbers'

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Learn to find the greatest common factor of two
or more whole numbers.
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Insert Lesson Title Here
Vocabulary
greatest common factor (GCF)
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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.
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Additional Example 1 Using a List to Find the GCF
Find the greatest common factor (GCF).
12, 36, 54
List all of the factors of each number.
12 1, 2, 3, 4, 6, 12
36 1, 2, 3, 4, 6, 9, 12, 18, 36
Circle the greatest factor that is in all the
lists.
54 1, 2, 3, 6, 9, 18, 27, 54
The GCF is 6.
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Try This Example 1
Find the greatest common factor (GCF).
14, 28, 63
List all of the factors of each number.
14 1, 2, 7, 14

28 1, 2, 4, 7, 14, 28
Circle the greatest factor that is in all the
lists.
63 1, 3, 7, 9, 21, 63
The GCF is 7.
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Additional Example 2A Using Prime Factorization
to Find the GCF
Find the greatest common factor (GCF).
A. 40, 56
Write the prime factorization of each number and
circle the common factors.
40 2 2 2 5
56 2 2 2 7
2 2 2 8
Multiply the common prime factors.
The GCF is 8.
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Additional Example 2B Using Prime Factorization
to Find the GCF
Find the greatest common factor (GCF).
B. 252, 180, 96, 60
Write the prime factorization of each number and
circle the common prime factors.
252 2 2 3 3 7
180 2 2 3 3 5
96 2 2 2 2 2 3
60 2 2 3 5
2 2 3 12
Multiply the common prime factors.
The GCF is 12.
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Try This Example 2A
Find the greatest common factor (GCF).
A. 72, 84
72 2 2 2 9
Write the prime factorization of each number and
circle the common factors.
84 2 2 7 3
2 2 4
Multiply the common prime factors.
The GCF is 4.
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Try This Example 2B
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 the common prime factors.
250 2 5 5 5
170 2 5 17
40 2 2 2 5
Multiply the common prime factors.
2 5 10
The GCF is 10.
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Additional Example 3 Problem Solving Application
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?
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Additional Example 3 Continued
Rewrite the question as a statement.
Find the greatest number of matching bracelets
you can make.
List the important information
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.
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Additional Example 3 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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Additional Example 3 Continued
If you make 5 bracelets, each one will have 24
red beads, 20 white beads, and 9 blue beads, with
nothing left over.
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Try This Example 3
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?
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Try This Example 3 Continued
Rewrite the question as a statement.
Find the greatest number of sets of flies
he can make.
List the important information
There are 24 wet flies and 18 dry flies.
He must use all of the flies.
The answer will be the GCF of 24 and 18.
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Try This Example 3 Continued
You can list the prime factors of 24 and 18 to
find the GCF.
24 2 2 2 3 18 2 3 3
Multiply the prime factors that are common to
both 24 and 18.
2 3 6
You can make 6 sets of flies.
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Try This Example 3 Continued
If you make 6 sets, each set will have 3 dry
flies and 4 wet flies.
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Lesson Quiz Part 1
Find the greatest common factor (GCF). 1. 28, 40
2. 24, 56 3. 54, 99 4. 20, 35, 70
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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?
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