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EXAMPLE 2

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

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EXAMPLE 2

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  1. 2 2 5 3 3 180 = 2 3 7 126 = 3 ANSWER The common prime factors of 180 and 126 are 2, 3, and 3. So, the greatest common factor is 2 32 = 18. 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.

  2. ANSWER The common prime factors of 180 and 126 are 2, 3, and 3. So, the greatest common factor is 2 32 = 18. EXAMPLE 2 Using Prime Factorization to Find the GCF

  3. Factors of28: 1, 2, 4, 7, 14, 28 Factors of45: 1, 3, 5, 9, 15, 45 The GCF is 1. ANSWER Because the GCF is 1, 28 and 45 are relatively prime. Factors of15: 1, 3,5, 15 Factors of51: 1, 3, 17, 51 The GCF is 3. ANSWER Because the GCF is 3, 15 and 51 are not relatively prime. EXAMPLE 3 Identifying Relatively Prime Numbers Tell whether the numbers are relatively prime. a. 28, 45 b.15, 51

  4. ANSWER ANSWER ANSWER ANSWER 30 12 24 1 GUIDED PRACTICE GUIDED PRACTICE for Example 2 and 3 Find the greatest common factor of the numbers using prime factorization. 6.90, 150 7.84, 216 8.120, 192 9.49, 144

  5. ANSWER ANSWER ANSWER ANSWER yes yes no no GUIDED PRACTICE GUIDED PRACTICE for Example 2 and 3 Tell whether the numbers are relatively prime. 6.13, 24 7.16, 25 8.38, 48 9.125, 175

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