Definition:Greatest Common Divisor/Real Numbers

Definition
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 $b$ (abbreviated GCD or gcd) and denoted $\gcd \set {a, b}$.

Also see

 * Greatest Common Measure of Commensurable Magnitudes where its existence is proven.