# gcd 0 0 = 0

**Marc van Dongen
**
dongen@cs.ucc.ie

*Fri, 14 Dec 2001 12:38:58 +0000*

Simon Peyton Jones (simonpj@microsoft.com) wrote:
:* If someone could write a sentence or two to explain why gcd 0 0 = 0,
*:* (ideally, brief ones I can put in the report by way of explanation),
*:* I think that might help those of us who have not followed the details
*:* of the discussion.
*
Division in the context of gcds (of integers) is usually defined
along the lines of:
An integer $a$ divides integer $b$ if there exists an integer
$c$ such that $a c= b$.
Note that here division is a *relation* an not a *function*/*operator*.
Given the definition of division being a relation it makes perfect
sense to say that $0$ divides $0$ which is why
gcd 0 0 = 0; and
gcd 0 0 /= error "Blah"
The gcd of two integers is usually defined as a non-negative
number to make it unique.
HTH.
PS: I am strongly in favour of gcd 0 0 = 0.
Regards,
Marc van Dongen