GCD with Zero

Theorem
Let $a \in \Z$ be an integer such that $a \ne 0$.

Then:
 * $\gcd \left\{{a, 0}\right\} = \left\lvert{a}\right\rvert$

where $\gcd$ denotes greatest common divisor (GCD).

Proof
Follows from:
 * Integer Divides Zero
 * GCD for Negative Integers.