## Quick Reference

For two non-zero integers *a* and *b*, any integer that is a divisor of both is a common divisor. Of all the common divisors, the greatest is the greatest common divisor (or g.c.d.), denoted by (*a*, *b*). The g.c.d. of *a* and *b* has the property of being divisible by every other common divisor of *a* and *b*. It is an important theorem that there are integers *s* and *t* such that the g.c.d. can be expressed as *sa*+*tb*. If the prime decompositions of *a* and *b* are known, the g.c.d. is easily found: for example, if *a*=168=2^{3}×3×7 and *b*=180=2^{2}×3^{2}×5, then the g.c.d. is 2^{2}×3=12. Otherwise, the g.c.d. can be found by the Euclidean Algorithm, which can be used also to find *s* and *t* to express the g.c.d. as *sa*+*tb*. Similarly, any finite set of non-zero integers *a*_{1}, *a*_{2},…, *a*_{n} has a g.c.d., denoted by (*a*_{1}, *a*_{2},…, *a*_{n}), and there are integers *s*_{1}, *s*_{2},…, *s*_{n} such that this can be expressed as *s*_{1}*a*_{1}+*s*_{2}*a*_{2}+…+*s*_{n}*a*_{n}.

*Subjects:*
Mathematics.

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