When the two numbers of GCD are very long,

Euclidean algorithm will take longer time to compute GCD.

We have used

Euclidean Algorithm [15] 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 [24] 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).