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Holt CA Course 1

3-2 Greatest Common Divisor

Warm UpWarm Up

California StandardsCalifornia Standards

Lesson PresentationLesson Presentation

PreviewPreview

Holt CA Course 1

3-2 Greatest Common Divisor

Warm UpWrite 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

Holt CA Course 1

3-2 Greatest Common Divisor

NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form of a fraction).

California Standards

Holt CA Course 1

3-2 Greatest Common Divisor

The greatest common divisor (GCD) of two or more whole numbers is the greatest whole number that divides evenly into each number.

One way to find the GCD of two or more numbers is to list all the factors of each number. The GCD is the greatest factor that appears in all the lists.

Holt CA Course 1

3-2 Greatest Common Divisor

Vocabulary

greatest common divisor (GCD)

Holt CA Course 1

3-2 Greatest Common Divisor

Find the greatest common divisor (GCD) of 12, 36, and 54.

Additional Example 1: Using a List to Find the GCD

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

The GCD is 6.

List all of the factors of each number.

Circle the greatest factor that is in all the lists.

Holt CA Course 1

3-2 Greatest Common Divisor

Find the greatest common divisor (GCD).

Additional Example 2A: Using Prime Factorization to Find the GCD

40, 56

2 2 2 = 8

The GCD is 8.

Write the prime factorization of each number and circle the common prime factors.

Multiply the common prime factors.

40 = 2 2 2 5

56 = 2 2 2 7

Holt CA Course 1

3-2 Greatest Common Divisor

Find the greatest common divisor (GCD).

Additional Example 2B: Using Prime Factorization to Find the GCD

252, 180, 96, 60

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 GCD is 12.

Write the prime factorizationof each number and circlethe common prime factors.

Multiply the common primefactors.

Holt CA Course 1

3-2 Greatest Common Divisor

You have 120 red beads, 100 white beads, and 45 blue beads. You want to use all the beads to make identical bracelets that have red, white, and blue beads on each. What is the greatest number of matching bracelets you can make?

Additional Example 3: Problem Solving Application

Holt CA Course 1

3-2 Greatest Common DivisorAdditional 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 GCD of 120, 100, and 45.

Holt CA Course 1

3-2 Greatest Common Divisor

22 Make a Plan

You can list the prime factors of 120, 100,and 45 to find the GCD.

Solve33

120 = 2 2 2 3 5

100 = 2 2 5 5

45 = 3 3 5

The GCD of 120, 100, and 45 is 5.

You can make 5 bracelets.

Additional Example 3 Continued

Holt CA Course 1

3-2 Greatest Common Divisor

Look Back44

If you make 5 bracelets, each one will have 24 red beads, 20 white beads, and 9 bluebeads, with no beads left over.

Additional Example 3 Continued

Holt CA Course 1

3-2 Greatest Common Divisor

Check It Out! Example 1

Find the greatest common divisor of 14, 28, and 63.

14: 1, 2, 7, 14

28: 1, 2, 4, 7, 14, 28

63: 1, 3, 7, 9, 21, 63

The GCD is 7.

List all of the factors of each number.

Circle the greatest factor that is in all the lists.

Holt CA Course 1

3-2 Greatest Common Divisor

Check It Out! Example 2B

Find the greatest common divisor (GCD).

360, 250, 170, 40

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 GCD is 10.

Write the prime factorizationof each number and circle the common prime factors.

Multiply the common primefactors.

Holt CA Course 1

3-2 Greatest Common Divisor

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?

Holt CA Course 1

3-2 Greatest Common DivisorCheck It Out! Example 3 Continued

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 GCD of 24 and 18.

Holt CA Course 1

3-2 Greatest Common Divisor

22 Make a Plan

You can list the prime factors of 24 and 18 to find the GCD.

Check It Out! Example 3 Continued

Solve33

24 = 2 2 2 3

18 = 2 3 3

You can make 6 sets of flies.

2 3 = 6Multiply the prime factors that are common to both 24 and 18.

Holt CA Course 1

3-2 Greatest Common Divisor

Check It Out! Example 3 Continued

Look Back44

If you make 6 sets, each set will have 3 dry flies and 4 wet flies.

Holt CA Course 1

3-2 Greatest Common DivisorLesson Quiz

Find the greatest common divisor (GCD).

1. 28, 40 2. 24, 56

3. 54, 99 4. 20, 35, 70

84

9 5

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, Williams has 24 members, and Fulton has 72 members? 8

Holt CA Course 1

3-2 Greatest Common Divisor

Check It Out! Example 2A

Find the greatest common divisor (GCD).

72, 84

72 = 2 2 2 3 3

84 = 2 2 7 3

2 2 3 = 12

The GCD is 12.

Write the prime factorization of each number and circle the common prime factors.

Multiply the common prime factors.