CBSE Class 10 Answered

The Euclidean algorithm has many theoretical and practical applications.

It may be used to generate almost all the most important traditional musical rhythms used in different cultures throughout the world.

It is a key element of the RSA algorithm, a public-key encryption method widely used in electronic commerce. It is used to solve Diophantine equations, such as finding numbers that satisfy multiple congruences (Chinese remainder theorem) or multiplicative inverses of a finite field.

 The Euclidean algorithm can also be used in constructing continued fractions, in the Sturm chain method for finding real roots of a polynomial, and in several modern integer factorization algorithms.

 Finally, it is a basic tool for proving theorems in modern number theory, such as Lagrange's four-square theorem and the fundamental theorem of arithmetic (unique factorization).

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