# Euclidean Algorithm

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## euclidean algorithm

[yü′klid·ē·ən ′al·gə‚rith·əm]
(mathematics)
A method of finding the greatest common divisor of a pair of integers.

## Euclidean Algorithm

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When the two numbers of GCD are very long, Euclidean algorithm will take longer time to compute GCD.
We have used Euclidean Algorithm  to compute the greatest common devisor (GCD) between two non-negative integers.
Chapter 3 uses the Euclidean algorithm to find the reduced form of factions through prime factorization, prove certain divisibility shortcuts, and prove the fundamental theorem of arithmetic.
This is often computed using the extended Euclidean algorithm.
One could use the same argument that Feinstein uses to "prove" that it is impossible to determine in polynomial-time whether this equation has a solution, when in fact one can use the Euclidean algorithm to determine this information in polynomial-time.
Zhou, "A method for blind recognition of convolution code based on euclidean algorithm," in Proceedings of the 3rd International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM '07), pp.
where the inverse was computed using the Euclidean algorithm in the ring of integers modulo p.
The Euclidean algorithm for finding the greatest common divisor is applicable.
This type of modular multiplication is closely related to the Euclidean algorithm that determines the greatest common divisor between two integers by a process of successive division by the remainder from the previous operation.
The extended Euclidean algorithm  is an extension to the Euclidean algorithm.
Errors have been corrected in the third edition and parts of the Fast Euclidean Algorithm chapter have been refreshed.
Written for elementary school teachers (and presumably teachers in training), this textbook addresses numbers and operations in the mathematics curriculum of grades K-6 (as well as some topics that may be more appropriate for grades 7 and 8, such as rational numbers, the Euclidean Algorithm, and the conversion of a fraction to a decimal).

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