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Published byAriel Carson Modified about 1 year ago

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

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

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GUIDED PRACTICE Find the greatest common factor of the numbers using prime factorization , 150 GUIDED PRACTICE for Example 2 and 3 ANSWER , 216 ANSWER , 192 ANSWER , 144 ANSWER 1

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

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