Question

how to verify Euclid division algorithm​

Answer 1

Answer:

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. The basis of the Euclidean division algorithm is Euclid's division lemma.

Euclid's lemma — If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a and b. For example, if p = 19, a = 133, b = 143, then ab = 133 × 143 = 19019, and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well.

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