Definition:Greatest Common Divisor

Integers
When the integral domain in question is the integers $\Z$, the GCD is often defined differently, as follows:

Real Numbers
The concept can be extended to the set of real numbers:

Also see

 * Elements of Euclidean Domain have Greatest Common Divisor where it is shown that any two GCDs of $a$ and $b$ are associates.


 * Definition:GCD Domain