This calculator is designed for students and professionals who need to compute the greatest common divisor (gcd) and the coefficients of the extended Euclidean algorithm. It simplifies complex calculations in number theory.
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Data Source and Methodology
This tool is based on the mathematical principles described in the Wikipedia article on the Extended Euclidean Algorithm. All calculations adhere strictly to these well-established formulas.
The Formula Explained
\( ax + by = \gcd(a, b) \)
Where \( x \) and \( y \) are the coefficients found using the extended Euclidean algorithm.
Glossary of Terms
- gcd: Greatest common divisor of two numbers.
- Coefficients: Numbers x and y in the equation \( ax + by = \gcd(a, b) \).
How It Works: A Step-by-Step Example
To find the gcd and coefficients for a = 56 and b = 15, the algorithm performs the following steps...
Frequently Asked Questions (FAQ)
What is the extended Euclidean algorithm?
It is an extension of the Euclidean algorithm that finds integers x and y such that ax + by = gcd(a, b).
How do you calculate gcd using this algorithm?
By repeatedly applying the Euclidean algorithm while tracking the coefficients.