Euclidean Algorithm 
Common divisors of \(a\) and \(b\) when \(a\) is a multiple of \(b\)
If \(a\) is a multiple of \(b\), then every divisor of \(b\) is a divisor of \(a\).
Why?
Because, if \(d\) is a divisor of \(b\), then \(b=kd\), for some \(k\); if, moreover, \(a=lb\), then \(a=l\left(kd\right)=\left(lk\right)d\), hence \(d\) is a divisor of \(a\). For example, \(30\) is a multiple of \(6\) \((30=5\times6)\) and \(2\) is a divisor of \(6\) \((6=3\times2);\) \(2\) is a divisor of \(30\) \((30=5\times3\times2).\)
Therefore the common divisors of \(a\) and \(b\) are the divisors of \(b\).
