Lecture: The Euclidean Algorithm

This lecture discusses one of the earliest and most important mathematical algorithms. The Euclidean algorithm computes the greatest common divisor of two integers (it can be extended to other domains such as polynomials). This algorithm, not commonly taught when gcds are introduced in High School mathematics, is a much more efficient way to compute the gcd than using integer factorization.
The algorithm can be stated in a few lines, using recursion, yet it has many fascinating properties, and its complete analysis was a major undertaking.
An immediate generalization of the Euclidean algorithm, called the extended Euclidean algorithm computes integers x and y such that x*a + y*b = gcd(a,b).

Background Material



Maple worksheets and other resources


This assignment is a practice assignment not intended to be handed in.
Created: Sept. 21, 2010 by jjohnson AT cs DOT drexel DOT edu