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.