\begin{definition}[Definition:Common Divisor/Integral Domain]
Let $\struct {D, +, \times}$ be an integral domain.
Let $S \subseteq D$ be a finite subset of $D$.
Let $c \in D$ 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}