\begin{definition}[Definition:Greatest Common Divisor/Integers/Definition 1]
Let $a, b \in \Z: a \ne 0 \lor b \ne 0$.
The '''greatest common divisor of $a$ and $b$''' is defined as:
:the largest $d \in \Z_{>0}$ such that $d \divides a$ and $d \divides b$
where $\divides$ denotes divisibility.
This is denoted $\gcd \set {a, b}$.
\end{definition}