One is Common Divisor of Integers

Theorem
Let $a, b \in \Z$ be integers.

Then $1$ is a common divisor of $a$ and $b$.

Proof
From One Divides all Integers:
 * $1 \divides a$

and:
 * $1 \divides b$

where $\divides$ denotes divisibility.

The result follows by definition of common divisor.