Euclid’s Division Lemma

It is basically the restatement of the usual division system. The formal statement for this is-

For each pair of given positive integers a and b, there exist unique whole numbers q and r which satisfies the relation

 a = bq + r, 0 ≤ r < b, where q and r can also be Zero.

Where ‘a’ is a dividend, ‘b’ is divisor, ‘q’ is quotient and ‘r’ is remainder.

∴ Dividend = (Divisor \times Quotient) + Remainder

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