will any divisor of $0<a,b$ also divide $\gcd(a,b)$?

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Will any divisor of both $a,b>0$ also divide $\gcd(a,b)$?

Anyone have a proof of this if it is true, or counter in case of false? thanks,

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Because the greatest common divisor of two integers is a linear combination of them. See the link kindly provided below.