# GCD with Zero

## Theorem

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

Then:

$\gcd \set {a, 0} = \size a$

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

## Proof

Follows from:

Integer Divides Zero

and:

GCD for Negative Integers.

$\blacksquare$