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

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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.

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.

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.

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

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

If the factorization includes the number 2, it's even. If not, it's odd.

Coprimes, or relative primes, are two or more numbers that share no common divisors. To determine whether numbers are relatively prime, find their greatest common denominaotr. If it's one, they're coprime.

let's have two numbers a and b and a set of primes (pi) Suppose a = pa pa+1pa+2... and b = pb pb+1 pb+2... If at least one pi in both factorization is in common then the two numbers are not coprime (relatively prime), if none is in common then they are coprime

Very easily: if the prime factorization includes 2, it's even. If not, it's odd.

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