GCD of Integers with Common Divisor/Proof 1

Proof
Consider the demonstration of the operation of the Euclidean Algorithm applied to $a$ and $b$.

Let each equation be multiplied by $k$.

We have:

This is the operation of the Euclidean Algorithm applied to $k a$ and $k b$.

Hence the greatest common divisor is the last non-zero remainder $r_n k$.

That is:
 * $\gcd \set {k a, k b} = k \gcd \set {a, b}$