Greatest Common Divisor of Integers/Examples/-8 and -36

Example of Greatest Common Divisor of Integers
The greatest common divisor of $-8$ and $-36$ is:
 * $\gcd \set {-8, -36} = 4$

Proof
The strictly positive divisors of $-8$ are:
 * $\set {x \in \Z_{>0}: x \divides \paren {-8} } = \set {1, 2, 4, 8}$

The strictly positive divisors of $-36$ are:
 * $\set {x \in \Z_{>0}: x \divides \paren {-36} } = \set {1, 2, 3, 4, 6, 9, 12, 18, 36}$

Of these, the common divisors are:
 * $\set {x \in \Z_{>0}: x \divides \paren {-8} \land x \divides \paren {-36} } = \set {1, 2, 4}$

The greatest of these is $4$.