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**Begin by writing the prime factorization of each number.**

EXAMPLE 2 Using Prime Factorization to Find the GCF Find the greatest common factor of 180 and 126 using prime factorization. Begin by writing the prime factorization of each number. 180 = 2 3 5 126 = 2 3 7 ANSWER The common prime factors of 180 and 126 are 2, 3, and 3. So, the greatest common factor is = 18.

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EXAMPLE 2 Using Prime Factorization to Find the GCF ANSWER The common prime factors of 180 and 126 are 2, 3, and 3. So, the greatest common factor is = 18.

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**Tell whether the numbers are relatively prime.**

EXAMPLE 3 Identifying Relatively Prime Numbers Tell whether the numbers are relatively prime. Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 45: 1, 3, 5, 9, 15, 45 The GCF is 1. a. 28, 45 ANSWER Because the GCF is 1, 28 and 45 are relatively prime. Factors of 15: 1, 3, 5, 15 Factors of 51: 1, 3, 17, 51 The GCF is 3. b. 15, 51 ANSWER Because the GCF is 3, 15 and 51 are not relatively prime.

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**GUIDED PRACTICE GUIDED PRACTICE**

for Example 2 and 3 Find the greatest common factor of the numbers using prime factorization. 6. 90, 150 ANSWER 30 7. 84, 216 ANSWER 12 8. 120, 192 ANSWER 24 9. 49, 144 ANSWER 1

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**Tell whether the numbers are relatively prime.**

GUIDED PRACTICE GUIDED PRACTICE for Example 2 and 3 Tell whether the numbers are relatively prime. 6. 13, 24 ANSWER yes 7. 16, 25 ANSWER yes 8. 38, 48 ANSWER no 9. 125, 175 ANSWER no

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Factors and the Greatest Common Factor

Factors and the Greatest Common Factor

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