Hello Im having some trouble with this proof I can prove wit

Hello, I\'m having some trouble with this proof. I can prove with with Bézout\'s lemma, but am told there is a way to prove it without anything other than the GCD theorem, and the divisor theroem. Can someone please help me? Thanks!

Let c, d, f and g be integers. If gcd(f, g) = d and c > 0, then gcd(fc, gc) = dc.

Solution

Answer:

Let c, d, f and g be integers.

If gcd(f, g) = d then d/f and d/g implies that for any c>0 dc/fc and dc/fc

which implies that dc is the greatest common divisor of fc and gc.