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EXAMPLE 2

SOLUTION. Write the prime factorization of each number. Then look for all the common prime factors. 112 = 2 4 7. 45 = 3 2 5. EXAMPLE 2. Identifying Relatively Prime Numbers. Tell whether the numbers 112 and 45 are relatively prime.

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EXAMPLE 2

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  1. SOLUTION Write the prime factorization of each number. Then look for all the common prime factors. 112 = 24 7 45 = 32 5 EXAMPLE 2 Identifying Relatively Prime Numbers Tell whether the numbers 112 and 45 are relatively prime. There are no common prime factors. However, two numbers always have 1 as a common factor. So, the GCF is 1.

  2. ANSWER The numbers 112 and 45 are relatively prime. EXAMPLE 2 Identifying Relatively Prime Numbers

  3. Pep Rally Students at your school are planning to hand out pep rally packs to support your school’s athletic program. The students have 240 bumper stickers, 360 pennants, and 720 pencils. Every pack must have the same contents, and no items should be left over. What is the greatest number of packs that can be made? What will each pack contain? EXAMPLE 3 Solve a Multi-Step Problem

  4. STEP 1 Find the greatest number of pep rally packs by finding the GCF. 240 = 24 3 5 360 = 23 32 5 720 = 24 32 5 The common prime factors are 23, 3 and 5. The GCF is 23 3 5, or 120. So, 120 pep rally packs can be made. EXAMPLE 3 Solve a Multi-Step Problem

  5. STEP 2 Divide the number of items by the number of pep rally packs. 240 120 = 2 360 120 = 3 720 120 = 6 ANSWER The greatest number of pep rally packs is 120. Each pack will contain 2 bumper stickers, 3 pennants, and 6 pencils. EXAMPLE 3 Solve a Multi-Step Problem

  6. for Examples 2 and 3 GUIDED PRACTICE Tell whether the numbers are relatively prime. If they are not relatively prime, find the GCF. 5. 48, 72

  7. ANSWER The number 48 and 72 are not relatively prime. The GCF is 23 3, or 24 for Examples 2 and 3 GUIDED PRACTICE

  8. for Examples 2 and 3 GUIDED PRACTICE Tell whether the numbers are relatively prime. If they are not relatively prime, find the GCF. 6. 124, 128

  9. ANSWER The numbers 124 and 128 are not relatively prime. The GFC is 22 or 4 for Examples 2 and 3 GUIDED PRACTICE

  10. for Examples 2 and 3 GUIDED PRACTICE Tell whether the numbers are relatively prime. If they are not relatively prime, find the GCF. 7. 39, 44

  11. ANSWER The numbers 39 and 44 are relatively prime. for Examples 2 and 3 GUIDED PRACTICE

  12. for Examples 2 and 3 GUIDED PRACTICE Tell whether the numbers are relatively prime. If they are not relatively prime, find the GCF. 8. 200, 63

  13. ANSWER The numbers 200 and 63 are relatively prime. for Examples 2 and 3 GUIDED PRACTICE

  14. ANSWER The greatest number of pep rally packs is 120. Each pack will contain 2 bumper stickers, 3 pennants, and 6 pencils. for Examples 2 and 3 GUIDED PRACTICE 9. What If? In Example 3, suppose the students have 240 bumper stickers and 360 pennants, but only 600 pencils. How many pep rally packs can be made? What items will each pack contain?

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