\begin{definition}[Definition:Greatest Common Divisor/Integers/Definition 2]
Let $a, b \in \Z: a \ne 0 \lor b \ne 0$.
The '''greatest common divisor of $a$ and $b$''' is defined as the (strictly) positive integer $d \in \Z_{>0}$ such that:
:$(1): \quad d \divides a \land d \divides b$
:$(2): \quad c \divides a \land c \divides b \implies c \divides d$
where $\divides$ denotes divisibility.
This is denoted $\gcd \set {a, b}$.
\end{definition}