Question

Q. What is the difference between ' Euclid's Division Lemma ' and ' Euclid's Division Algorithm ' ?

Q. What is the use of both of these ?

Answer 1

Heya!

Here is yr answer........

=> What is the diff. between "Euclid's division lemma" and "Euclid's division algorithm"??

Answer :-
~~~~~~~

Euclid's division lemma is the basis or introduction for the Euclid's division algorithm...
The Euclid's division lemma is done in '1' step.. whereas the Euclid's division algorithm is done in more than one step.. (it depends on the values a, b).

=> What is the use of both of these??

Answer :-
~~~~~~~

The both Euclid's division lemma and the Euclid's division algorithm is used to find the HIGHEST COMMON FACTOR (HCF) of two values (a, b) by using ----

a = bq + r ( 0</= r<b)

Hope it helps.....

#BeBrainly...

Answer 2

Lemma is a proven statement used for proving another statement while algorithm is a series of well defined steps which gives a procedure for solving a type of a problem.

 

Euclid's division lemma: For given any positive integers a and b there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.

 

Euclid's division algorithm is used for finding the Highest Common Factor of two numbers where in we apply the statement of Euclid's division lemma