Question

If gcd(a,b)=1 then prove that gcd(ab,c)=gcd(a,c)xgcd(b,c)

Answer 1

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Answer 2

Think about the prime factorization of \(a \cdot b\). The key is that they are disjoint since they are coprime. There are no prime factors common to \(a\) and \(b\). So then then for each factor in the gcd must lie either in the prime factorization of \(a\) or the prime factorization of \(b\)

Answer 3

in proof form? GCD-CT EEA GCD-OO