Question

what is the difference between Euclid's division lemma and Euclid's division algorithm

Answer 1

Hi,
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 , Here we can say q = quotient and " r " is remainder

Euclid Division Algorithm is a method 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.