That page explains how to construct a table using the Euclidean Algorithm. In the Extended Euclidean Algorithm we're going to do the same, but with some extra columns in the table.

The Euclidean algorithm is basically a continual repetition of the division algorithm for integers. The point is to repeatedly divide the divisor by the remainder until the remainder is 0.

The extended Euclidean algorithm is the essential tool for computing multiplicative inverses in modular structures, typically the modular integers and the algebraic field extensions.

Learn the Extended Euclidean Algorithm step by step and discover how it is used to compute the modular multiplicative inverse, with detailed examples, diagrams, and Python code.

Example of Extended Euclidean Algorithm Recall that gcd(84, 33) = gcd(33, 18) = gcd(18, 15) = gcd(15, 3) = gcd(3, 0) = 3 We work backwards to write 3 as a linear combination of 84 and 33:

Oct 12, 2025 · We found the values of x and y : The recursive function above returns the GCD and the values of coefficients to x and y (which are passed by reference to the function). This …

Feb 17, 2025 · The extended Euclidean algorithm updates the results of gcd (a, b) using the results calculated by the recursive call gcd (b%a, a). Let values of x and y calculated by the …

The Extended Euclidean Algorithm is the most primitive of these algorithms and essential for students. In this article, I will explain use this algorithm on a few example problems, hopefully …

Similarly, the polynomial extended euclidean algorithm lets one to calculate the multiplicative inverse in algebraic field extensions and, in particular in finite fields of non prime order.

Rather than give a set of equations, we'll show how it works with the two examples we calclated in Section 3.1.3. For the Extended Euclidean Algorithm, we'll form a table with three columns and …