(algorithm)

**Definition:**
An algorithm to find the *greatest common divisor*, *g*, of two positive integers, *a* and *b*, and coefficients, *h* and *j*, such that *g = ha + jb*.

**See also**
*Euclid's algorithm*.

*Note:
These coefficients are useful for computing modular multiplicative inverses. After [CLR90, page 811].*

Author: PEB

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Entry modified 17 December 2004.

HTML page formatted Fri Feb 23 10:06:07 2018.

Cite this as:

Paul E. Black, "extended Euclid's algorithm", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/extendEuclid.html