Greatest Common Factors

1. 2-7 Greatest Common Factor
Course 2
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2. 2-7 Greatest Common Factor
Warm Up
Write the prime factorization of each
number.
1. 20
22 · 5
2. 100
22 · 52
3. 30
2 · 3 · 5
4. 128
5. 70
Course 2
27
2 · 5 · 7

3. 2-7 Greatest Common Factor
Problem of the Day: Part I
Use the clues to find the numbers
being described.
1. a. The greatest common factor (GCF)
of two numbers is 5.
b. The sum of the numbers is 75.
c. The difference between the
numbers is 5.
35 and 40
Course 2

4. 2-7 Greatest Common Factor
Problem of the Day: Part II
Use the clues to find the numbers being
described.
2. a. The GCF of three different numbers
is 4.
b. The sum of the numbers is 64.
Possible answer: 12, 16, 36
Course 2

5. 2-7 Greatest Common Factor
Learn to find the greatest common factor
of two or more whole numbers.
Course 2

6. 2-7 Greatest Insert Lesson Common Title Factor
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Vocabulary
greatest common factor (GCF)
Course 2

7. 2-7 Greatest Common Factor
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.
Course 2

8. 2-7 Greatest Common Factor
Additional Example 1: Using a List to Find the GCF
Find the greatest common factor (GCF) of 12,
36, 54.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
List all of the factors of each number.
Circle the greatest factor that is in all the lists.
The GCF is 6.
Course 2

9. 2-7 Insert Greatest Lesson Common Title Factor
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Check It Out: Example 1
Find the greatest common factor of 14, 28, 63.
List all of the factors of each number.
Circle the greatest factor that is in all the lists.
Course 2
14: 1, 2, 7, 14
28: 1, 2, 4, 7, 14, 28
63: 1, 3, 7, 9, 21, 63
The GCF is 7.

10. 2-7 Greatest Common Factor
Additional Example 2A: Using Prime Factorization to
Find the GCF
Find the greatest common factor (GCF).
40, 56
Course 2
40 = 2 · 2 · 2 · 5
56 = 2 · 2 · 2 · 7
2 · 2 · 2 = 8
The GFC is 8.
Write the prime factorization of
each number and circle the
common prime factors.
Multiply the common prime
factors.

11. 2-7 Greatest Common Factor
Additional Example 2B: Using Prime Factorization to
Find the GCF
Find the greatest common factor (GCF).
252, 180, 96, 60
Course 2
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
The GCF is 12.
Multiply the common prime
factors.

12. 2-7 Insert Greatest Lesson Common Title Factor
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Check It Out: Example 2A
Find the greatest common factor (GCF).
72, 84
Course 2
72 = 2 · 2 · 2 · 3 · 3
84 = 2 · 2 · 7 · 3
2 · 2 · 3 = 12
The GCF is 12.
Write the prime factorization
of each number and circle
the common prime factors.
Multiply the common prime
factors.

13. 2-7 Insert Greatest Lesson Common Title Factor
Here
Check It Out: Example 2B
Find the greatest common factor (GCF).
360, 250, 170, 40
Course 2
360 = 2 · 2 · 2 · 3 · 3 · 5
250 = 2 · 5 · 5 · 5
170 = 2 · 5 · 17
40 = 2 · 2 · 2 · 5
2 · 5 = 10
The GCF is 10.
Write the prime
factorization
of each number and
circle the common
prime factors.
Multiply the common prime
factors.

14. 2-7 Greatest Common Factor
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?
Course 2

15. 2-7 Greatest Common Factor
Additional Example 3 Continued
11 Understand the Problem
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.
Course 2

16. 2-7 Greatest Common Factor
Additional Example 3 Continued
22 Make a Plan
Course 2
You can list the prime factors of 120, 100,
and 45 to find the GFC.
33 Solve
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.

17. 2-7 Greatest Common Factor
Course 2
Additional Example 3 Continued
44 Look Back
If you make 5 bracelets, each one will have
24 red beads, 20 white beads, and 9 blue
beads, with nothing left over.

18. 2-7 Insert Greatest Lesson Common Title Factor
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Check It Out: 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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19. 2-7 Insert Greatest Lesson Common Title Factor
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Check It Out: Example 3 Continued
Course 2
11 Understand the Problem
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.

20. 2-7 Greatest Common Factor
Course 2
Check It Out: Example 3 Continued
22 Make a Plan
You can list the prime factors of 24 and 18
to find the GCF.
33 Solve
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.

21. 2-7 Insert Greatest Lesson Common Title Factor
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Check It Out: Example 3 Continued
Course 2
44 Look Back
If you make 6 sets, each set will have
3 dry flies and 4 wet flies.

22. 2-7 Greatest Insert Lesson Common Title Factor
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Lesson Quiz: Part I
Find the greatest common factor (GCF).
1. 28, 40
4
2. 24, 56
8
3. 54, 99
9
4. 20, 35, 70
5
Course 2

23. 2-7 Greatest Insert Lesson Common Title Factor
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Lesson Quiz: Part II
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?
Course 2
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