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Let a and b be positive integers. If c = gcd(a,b), prove that gcd(a/c,b/c) = 1
*Note that a/c and b/c are integers.
So I know that c|a and c|b and that a gcd of 1 implies that the resulting integers are relatively prime. I know this must be within a simple definition, however I am new to these type of proofs and I don't know how to start or conceptualize this one. Any help would be appreciated.