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Q: How can you determine whether the GCF of two numbers is one by looking at their prime factorization?

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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.

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

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

You CAN'T determine whether two numbers are proportional, just by looking at one number from each set.

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

You can determine whether the atoms are the same element with out looking at the nuclei. This can be done by testing for specific properties.

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

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

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