Explain Euclid Division Lemma.

Euclid's Division Lemma

It 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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