Question

what is difference between a euclid division Lemma and euclid division algorithm.?

Answer 1

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.

 

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Answer 2

According to Euclid's Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b. ...

Euclids Division Algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers. Recall that the HCF of two positive integers a and b is the largest positive integer d that divides both a and b.