\begin{definition}[Definition:Greatest Common Divisor/Integers/General Definition]
Let $S = \set {a_1, a_2, \ldots, a_n} \subseteq \Z$ such that $\exists x \in S: x \ne 0$ (that is, at least one element of $S$ is non-zero).
Then the '''greatest common divisor''' of $S$:
:$\gcd \paren S = \gcd \set {a_1, a_2, \ldots, a_n}$
is defined as the largest $d \in \Z_{>0}$ such that:
:$\forall x \in S: d \divides x$
where $\divides$ denotes divisibility.
\end{definition}