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Q: How can you use prime factorization to determine if two numbers 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 your numbers have no prime factors in common, they are relatively prime.

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

Keep dividing until all the factors are prime.

Most of the time. If you can recognize that the two numbers are relatively prime, factorization isn't necessary. Just multiply the two numbers together.

Prime factorization is a common mathematical tool. One uses prime factorization to determine what prime factors of any given number are. One can practice this tool online.

There is no need to do prime factorization as prime numbers are already prime.

Since prime numbers only have one prime factor (themselves), they don't have prime factorizations.

prime factorization is the factorization of numbers

Because the prime decomposition of primes is trivial and pointless.

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