Greatest Common Divisor of Integers/Examples/-5 and 5

Example of Greatest Common Divisor of Integers
The greatest common divisor of $-5$ and $5$ is:
 * $\gcd \set {-5, 5} = 5$

Proof
The strictly positive divisors of $-5$ are:
 * $\set {x \in \Z_{>0}: x \divides \paren {-5} } = \set {1, 5}$

The strictly positive divisors of $5$ are:
 * $\set {x \in \Z_{>0}: x \divides 5 } = \set {1, 5}$

Of these, the common divisors are:
 * $\set {x \in \Z_{>0}: x \divides \paren {-5} \land x \divides 5 } = \set {1, 5}$

The greatest of these is $5$.