1. Holt CA Course 1 3-2 Greatest Common Divisor Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 3-2 Greatest Common Divisor Warm Up Write the prime factorization of each number. 1. 20 2. 100 3. 30 4. 128 5. 70 2 2  5 2 2  5 2 2  3  5 2727 2  5  7

3. 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

4. Holt CA Course 1 3-2 Greatest Common Divisor Vocabulary greatest common divisor (GCD)

5. 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.

6. 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.

7. 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.

8. 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

9. 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 factorization of each number and circle the common prime factors. Multiply the common prime factors.

10. 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.

11. 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 factorization of each number and circle the common prime factors. Multiply the common prime factors.

12. 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

13. Holt CA Course 1 3-2 Greatest Common Divisor 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 GCD of 120, 100, and 45.

14. Holt CA Course 1 3-2 Greatest Common Divisor 2 Make a Plan You can list the prime factors of 120, 100, and 45 to find the GCD. Solve 3 120 = 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

15. Holt CA Course 1 3-2 Greatest Common Divisor Look Back 4 If you make 5 bracelets, each one will have 24 red beads, 20 white beads, and 9 blue beads, with no beads left over. Additional Example 3 Continued

16. 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?

17. Holt CA Course 1 3-2 Greatest Common Divisor Check It Out! 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 GCD of 24 and 18.

18. Holt CA Course 1 3-2 Greatest Common Divisor 2 Make a Plan You can list the prime factors of 24 and 18 to find the GCD. Check It Out! Example 3 Continued Solve 3 24 = 2  2  2  3 18 = 2  3  3 You can make 6 sets of flies. 2  3 = 6 Multiply the prime factors that are common to both 24 and 18.

19. Holt CA Course 1 3-2 Greatest Common Divisor Check It Out! Example 3 Continued Look Back 4 If you make 6 sets, each set will have 3 dry flies and 4 wet flies.

20. Holt CA Course 1 3-2 Greatest Common Divisor Lesson Quiz Find the greatest common divisor (GCD). 1. 28, 40 2. 24, 56 3. 54, 994. 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