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Q: How can you use prime factorization of two numbers to determine whether they are relatively prime?

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Use the prime factorizations to determine the GCF. If the GCF is 1, the numbers are relatively prime. If the two numbers have no prime factors in common, they are relatively prime.

If the prime factorizations contain no factors in common (their GCF is 1), the numbers are relatively prime.

If the prime factorizations have no prime factors in common, the numbers are relatively prime.

If the prime factorizations have no factors in common, the LCM is the product of them.

If there are no prime factors in common, the GCF is 1.

By trying out whether you can divide it by different numbers. For one- or two-digit numbers, it is enough to test divisibility by 2, 3, 5, 7.

Example: 36 and 175 2 x 2 x 3 x 3 = 36 5 x 5 x 7 = 175 There are no common prime factors. The GCF is 1. By definition, that makes them relatively prime.

Example: 4 and 9 2 x 2 = 4 3 x 3 = 9 No common prime factors. The GCF is 1. The numbers are relatively prime.

If the prime factorization contains a 5 and a 7, 35 is a factor.

Yes, if they have no common factors. Do the prime factorization for two numbers, and check whether they have, or don't have, common factors. Example: let one of the numbers be 2 x 3, the other 52. Since none of the numbers shares factors with the other one, they are relatively prime.

2 x 2 x 2 x 5 = 40 2 x 7 x 7 = 98 The GCF is 2. The numbers are not relatively prime.

If the two numbers have no common prime factors, the LCM will be the product of the numbers.

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