\begin{definition}[Definition:Common Divisor/Integers]
Let $S$ be a finite set of integers, that is:
:$S = \set {x_1, x_2, \ldots, x_n: \forall k \in \N^*_n: x_k \in \Z}$
Let $c \in \Z$ such that $c$ divides all the elements of $S$, that is:
:$\forall x \in S: c \divides x$
Then $c$ is a '''common divisor''' (or '''common factor''') of all the elements in $S$.
\end{definition}