Common Divisors

If d $\mid$ a and d $\mid$ b, then d is a common divisor of a and b. The greatest common divisor gcd(a,b) is the largest such common divisor d.

$$gcd(a,b) \;=\; \left\{ \begin{array}{ll} 0 & {\rm if} \; a =... ...mid a \mid, \mid b \mid) & {\rm otherwise} \end{array} \right.$$

For example, some common divisors of 12 and 18 are 1, 2, 3, and 6. The greatest common divisor of 12 and 18 is 6.