Lecture 5: The Euclidean Algorithm

This lecture introduces 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.

Background Material


Also study Maple's igcd, igcdex, gcd, and gcdex commands.


Maple worksheets and programs and other resources

Created: Oct. 20, 2005 by jjohnson@cs.drexel.edu