Euclid’s algorithm for finding the greatest common divisor of two numbers dates from the fourth century b.c. but remains one of the fastest algorithms available in modern computational number theory. In this chapter we look at Euclid’s algorithm and its immediate consequences, analyze its speed, and, as an interesting aside, discuss a speculative connection between Euclid’s algorithm and classical Greek proofs that √n is irrational when n is not a square.
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