Using Euclids Extended Algorithm:
Calculate x and y in Bézout's Identity
using (95,941094)
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 | 95 | |||
| Set to 0 | 0 | Set to 1 | 1 | 941094 | Quotient of 95/941094 | 0 | |
| 1 - (0 x 0) | 1 | 0 - (0 x 1) | 0 | Remainder of 95/941094 | 95 | Quotient of 941094/95 | 9906 |
| 0 - (9906 x 1) | -9906 | 1 - (9906 x 0) | 1 | Remainder of 941094/95 | 24 | Quotient of 95/24 | 3 |
| 1 - (3 x -9906) | 29719 | 0 - (3 x 1) | -3 | Remainder of 95/24 | 23 | Quotient of 24/23 | 1 |
| -9906 - (1 x 29719) | -39625 | 1 - (1 x -3) | 4 | Remainder of 24/23 | 1 | Quotient of 23/1 | 23 |
| 29719 - (23 x -39625) | 941094 | -3 - (23 x 4) | -95 | Remainder of 23/1 | 0 | Quotient of 1/0 | 0 |
Take the last non-zero row for d:
a = -39625 and b = 4
GCD Equation
ax + by = gcd(a,b)
95x + 941094y = gcd(95
Final Answer:
GCF(95, 941094) = 1
You have 2 free calculationss remaining
What is the Answer?
GCF(95, 941094) = 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.
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
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