# CBSE Class 10 Answered

**what is the variety of appliction on euclids division lemma and in allied science**

*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).*

*Regards,*

*Team,*

*TopperLearning.*