Finding the Greatest Common Factor Using Euclid's Algorithm

Learn about Euclid's algorithm for finding the greatest common divisor (GCD) of two positive integers in this 21-minute mathematics video. Explore the historical significance of this algorithm from Euclid's Elements (300 BC) and understand its improved version using division. Master the proof of the algorithm's validity, which guarantees efficiency with a maximum of 5k steps (where k is the number of digits of the smaller integer). Discover practical applications through visualizations and learn how to solve diophantine equations of the form ax+by=gcd. Progress through topics including the basic algorithm, its computational complexity, mathematical proof, visual representations, and methods for finding multiple solutions to related equations.