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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 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. 2 7. 2  5  7. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 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. California Standards 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).

  4. Vocabulary greatest common divisor (GCD)

  5. 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. Additional Example 1:Using a List to Find the GCD Find the greatest common divisor (GCD) of 12, 36, and 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 GCD is 6.

  7. 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 List all of the factors of each number. Circle the greatest factor that is in all the lists. The GCD is 7.

  8. Additional Example 2A: Using Prime Factorization to Find the GCD Find the greatest common divisor (GCD). 40, 56 Write the prime factorization of each number and circle the common prime factors. 40 = 2  2  2  5 56 = 2  2  2  7 2  2  2 = 8 Multiply the common prime factors. The GCD is 8.

  9. Additional Example 2B: Using Prime Factorization to Find the GCD Find the greatest common divisor (GCD). 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 GCD is 12.

  10. Check It Out! Example 2A Find the greatest common divisor (GCD). 72, 84 Write the prime factorization of each number and circle the common prime factors. 72 = 2  2  2  3  3 84 = 2  2  7  3 Multiply the common prime factors. 2  2  3 = 12 The GCD is 12.

  11. Check It Out! Example 2B Find the greatest common divisor (GCD). 360, 250, 170, 40 360 = 2  2  2  3  3  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 GCD is 10.

  12. 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 identical bracelets that have red, white, and blue beads on each. What is the greatest number of matching bracelets you can make?

  13. 1 Understand the Problem 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 GCD of 120, 100, and 45.

  14. 3 Solve Make a Plan 2 Additional Example 3 Continued You can list the prime factors of 120, 100, and 45 to find the GCD. 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.

  15. Look Back 4 Additional Example 3 Continued If you make 5 bracelets, each one will have 24 red beads, 20 white beads, and 9 blue beads, with no beads left over.

  16. 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. 1 Understand the Problem Check It Out! 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 GCD of 24 and 18.

  18. 3 Solve Make a Plan 2 Check It Out! Example 3 Continued You can list the prime factors of 24 and 18 to find the GCD. 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.

  19. Look Back 4 Check It Out! Example 3 Continued If you make 6 sets, each set will have 3 dry flies and 4 wet flies.

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