\begin{definition}[Definition:Greatest Common Divisor/Real Numbers]
Let $a, b \in \R$ be commensurable.
Then there exists a greatest element $d \in \R_{>0}$ such that:
: $d \divides a$
: $d \divides b$
where $d \divides a$ denotes that $d$ is a divisor of $a$.
This is called the '''greatest common divisor of $a$ and $b$''' and denoted $\gcd \set {a, b}$.
\end{definition}