\begin{definition}[Definition:Coprime/Euclidean Domain]
Let $\struct {D, +, \times}$ be a Euclidean domain.
Let $U \subseteq D$ be the group of units of $D$.
Let $a, b \in D$ such that $a \ne 0_D$ and $b \ne 0_D$
Let $d = \gcd \set {a, b}$ be the greatest common divisor of $a$ and $b$.
Then $a$ and $b$ are '''coprime''' {{iff}} $d \in U$.
That is, two elements of a Euclidean domain are '''coprime''' {{iff}} their greatest common divisor is a unit of $D$.
\end{definition}