Using Euclids Extended Algorithm:
Calculate x and y in Bézout's Identity
using (2,165)
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 | 2 | |||
| Set to 0 | 0 | Set to 1 | 1 | 165 | Quotient of 2/165 | 0 | |
| 1 - (0 x 0) | 1 | 0 - (0 x 1) | 0 | Remainder of 2/165 | 2 | Quotient of 165/2 | 82 |
| 0 - (82 x 1) | -82 | 1 - (82 x 0) | 1 | Remainder of 165/2 | 1 | Quotient of 2/1 | 2 |
| 1 - (2 x -82) | 165 | 0 - (2 x 1) | -2 | Remainder of 2/1 | 0 | Quotient of 1/0 | 0 |
Take the last non-zero row for d:
a = -82 and b = 1
GCD Equation
ax + by = gcd(a,b)
2x + 165y = gcd(2
Final Answer:
GCF(2, 165) = 1
What is the Answer?
GCF(2, 165) = 1
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.
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?
algorithmA process to solve a problem in a set amount of timeequationa statement declaring two mathematical expressions are equaleuclids algorithmmethod for computing the greatest common divisor (GCD) of two numberseuclids extended algorithmdivision algorithm for integersgreatest common factorlargest positive integer dividing a set of integersidentityan equality that holds true regardless of the values chosen for its variablesquotientThe result of dividing two expressions.remainderThe portion of a division operation leftover after dividing two integersExample calculations for the Euclids Algorithm and Euclids Extended Algorithm Calculator
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