1. Greatest Common Factor
2-5
Greatest Common Factor
Course 2
Warm Up
Problem of the Day
Lesson Presentation

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

3. Greatest Common Factor
Course 2
2-5
Greatest Common Factor
Problem of the Day: Part 1
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

4. Greatest Common Factor
Course 2
2-5
Greatest Common Factor
Problem of the Day: Part 2
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

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

6. Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
Vocabulary
greatest common factor (GCF)

7. Greatest Common Factor
Course 2
2-5
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.

8. Additional Example 1: Using a List to Find the GCF
Course 2
2-5
Greatest Common Factor
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.

9. Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
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.

10. Additional Example 2A: Using Prime Factorization to Find the GCF
Course 2
2-5
Greatest Common Factor
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 GFC is 8.

11. Additional Example 2B: Using Prime Factorization to Find the GCF
Course 2
2-5
Greatest Common Factor
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.

12. Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
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.

13. Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
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.

14. Additional Example 3: Problem Solving Application
Course 2
2-5
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?

15. Understand the Problem
Course 2
2-5
Greatest Common Factor
Additional Example 3 Continued 1
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.

16. Additional Example 3 Continued
Course 2
2-5
Greatest Common Factor
Additional Example 3 Continued 2
Make a Plan
You can list the prime factors of 120, 100,
and 45 to find the GFC.
Solve 3
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. Additional Example 3 Continued
Course 2
2-5
Greatest Common Factor
Additional Example 3 Continued
Look Back 4
If you make 5 bracelets, each one will have
24 red beads, 20 white beads, and 9 blue
beads, with nothing left over.

18. Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
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?

19. Understand the Problem
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
Try This: Example 3 Continued 1
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. Try This: Example 3 Continued
Course 2
2-5
Greatest Common Factor
Try This: Example 3 Continued 2
Make a Plan
You can list the prime factors of 24 and 18
to find the GCF.
Solve 3
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.

21. Greatest Common Factor Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
Try This: Example 3 Continued
Look Back 4
If you make 6 sets, each set will have
3 dry flies and 4 wet flies.

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

23. Greatest Common Factor Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
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