When 2 numbers have their GCF = 1, it means that the numbers are relatively prime to each other, which doesn't necessarily mean that they are prime on their own.
There are 2 cases where relative prime can be guarenteed:
All prime numbers are guarenteed to be relatively prime to all other prime numbers.
Any Prime number is guarenteed to be relatively prime to any composite number smaller than the prime number.
If neither of the above 2 conditions are met, manual calculations must be done to find any existing GCF.
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The GCF of these numbers is 1.
GCF(343, 512) = 1; the numbers are coprime.
The two numbers are coprime so the gcf is 1.
Since both the numbers are prime, their GCF is 1.
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