Greatest Common Divisor of Integers/Examples/20, 70 and 80

Example of Greatest Common Divisor of Integers
The greatest common divisor of $20$, $70$ and $80$ is:
 * $\gcd \set {20, 70, 80} = 10$

Proof
The strictly positive divisors of $20$ are:
 * $\set {x \in \Z_{>0}: x \divides 20} = \set {1, 2, 4, 5, 10, 20}$

The strictly positive divisors of $70$ are:
 * $\set {x \in \Z_{>0}: x \divides 70} = \set {1, 2, 5, 7, 10, 14, 35, 70}$

The strictly positive divisors of $80$ are:
 * $\set {x \in \Z_{>0}: x \divides 80} = \set {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}$

Of these, the common divisors are:
 * $\set {x \in \Z_{>0}: x \divides 20 \land x \divides 70 \land x \divides 80} = \set {1, 2, 5, 10}$

The greatest of these is $10$.