euclidean algorithm - OpenGenus IQ: Computing Expertise & Legacy

Extended Euclidean Algorithm

We will demonstrate Extended Euclidean Algorithm. We will see how you can calculate the greatest common divisor in a naive way which takes O(N) time complexity which we can improve to O(log N) time complexity using Euclid's algorithm. Extended Euclidean Algorithm takes O(log N) time complexity

greatest common divisor

Euclidean Algorithm to Calculate Greatest Common Divisor (GCD) of 2 numbers

The Euclid's algorithm (or Euclidean Algorithm) is a method for efficiently finding the greatest common divisor (GCD) of two numbers. The GCD of two integers X and Y is the largest integer that divides both of X and Y (without leaving a remainder).