Question

What is Euclid division algorithm. And lemma. Give difference .

Answer 1

Dear Student

We can write dividend as:–

Dividend = Divisor × Quotient + Remainder

Euclid's division Lemma :–

If a and b are positive integers, then there exist two unique integers q and r such that –

a = bq + r

This lemma is very useful for finding the H.C.F. of large numbers where braking them into factors is difficult.

On the other hand, Euclid Division Algorithm is a method/process to find H.C.F. of large numbers by using Euclid's Division Lemma.

Euclid division lemma is basically a proven statement which is used for proving other statements while Euclid Division algorithm is a technique to compute HCF of two given positive integers.

Regards