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
Extended Algorithm Table
| 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
GCD Equation
ax + by = gcd(a,b)
15x + 65y = gcd(15
Final Answer:
GCF(15, 65) = 5
What is the Answer?
GCF(15, 65) = 5
How does the Euclids Algorithm and Euclids Extended Algorithm Calculator work?
Free Euclids Algorithm and Euclids Extended Algorithm Calculator - 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.
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?
ax + by = d
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
