GCD with Zero

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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.

$\blacksquare$


Sources