(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

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 17 December 2004.

HTML page formatted Mon Feb 2 13:10:39 2015.

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: http://www.nist.gov/dads/HTML/extendEuclid.html