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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.


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

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.


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