GCD of Integers with Common Divisor/Corollary

Theorem
Let $a, b \in \Z$ be integers such that not both $a = 0$ and $b = 0$.

Let $k \in \Z_{\ne 0}$ be a non-zero integer.

Then:
 * $\gcd \set {k a, k b} = \size k \gcd \set {a, b}$

where $\gcd$ denotes the greatest common divisor.

Proof
From GCD of Integers with Common Divisor the case where $k > 0$ has been demonstrated.

It remains to demonstrate the case where $k < 0$.

Indeed:
 * $-k = \size k > 0$

and so: