What is Euclid's division algorithm?

Euclid's division algorithm: 

Euclid's Division Lemma states that if there are two positive integers a and b, then there exist unique integers q and r which satisfies the condition $a = bq + r$ where $0 ≤ r < b$

This can be understood by the following example:

We know that in any division problem: $Dividend = (Divisor \times Quotient) + Remainder$.

For example, if we divide 7 by 3:

Dividend $= 7$

Divisor $= 3$

Quotient $= 2$

Remainder $= 1$

For the numbers 7 and 3, there exist numbers 2 and 1 such that $7 = 2 \times 3 + 1$ where $0 ≤ 1 < 3$.

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Updated on: 10-Oct-2022

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