Common divisor ($d\mid a,d\mid b$)

A positive integer $d$ is a common divisor of integers $a,b$ when $d\mid a$ and $d\mid b$. For positive $a,b$, their largest common divisor is their greatest common divisor. The identity $a=qb+r$ implies that $a,b$ and $b,r$ have the same positive common divisors, because $r=a-qb$ and $a=qb+r$.