According to Euclid’s Division Lemma if we have two positive numbers a and b, then there are unique integers q and r which provides the condition a = bq + r where 0 ≤ r < b.

The source of the Euclidean group algorithm is Euclid’s division lemma. To determine the Highest Common Factor (HCF) of two real integers a and b we use Euclid’s division algorithm. HCF is the largest number that exactly divides two or more positive integers. That means, on dividing both the integers a and b the remainder is zero.

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