Using Euclids Extended Algorithm:

Calculate x and y in Bézout's Identity

using (15,65)

Bezouts Identity For 2 numbers a and b and divisor d:

ax + by = d

a math a b math b d math d k math k Set to 1 1 Set to 0 0 15 Set to 0 0 Set to 1 1 65 Quotient of 15/65 0 1 - (0 x 0) 1 0 - (0 x 1) 0 Remainder of 15/65 15 Quotient of 65/15 4 0 - (4 x 1) -4 1 - (4 x 0) 1 Remainder of 65/15 5 Quotient of 15/5 3 1 - (3 x -4) 13 0 - (3 x 1) -3 Remainder of 15/5 0 Quotient of 5/0 0

Take the last non-zero row for d: a =

-4 and b =

1 ax + by = gcd(a,b)

15x + 65y = gcd(15, 65)

GCF(15, 65) = 5

How does the Euclids Algorithm and Euclids Extended Algorithm Calculator work?
Given 2 numbers a and b, this calculates the following 1) The Greatest Common Divisor (GCD) using Euclids Algorithm 2) x and y in Bézouts Identity ax + by = d using Euclids Extended Algorithm
Extended Euclidean Algorithm This calculator has 2 inputs.

What 1 formula is used for the Euclids Algorithm and Euclids Extended Algorithm Calculator?
What 8 concepts are covered in the Euclids Algorithm and Euclids Extended Algorithm Calculator?
algorithm A process to solve a problem in a set amount of time equation a statement declaring two mathematical expressions are equal euclids algorithm method for computing the greatest common divisor (GCD) of two numbers euclids extended algorithm division algorithm for integers greatest common factor largest positive integer dividing a set of integers identity an equality that holds true regardless of the values chosen for its variables quotient The result of dividing two expressions. remainder The portion of a division operation leftover after dividing two integers
Example calculations for the Euclids Algorithm and Euclids Extended Algorithm Calculator Euclids Algorithm and Euclids Extended Algorithm Calculator Video VIDEO

Tags: Add This Calculator To Your Website