Question

what is division lemma
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Answer 1

>A Euclids division lemma is a proven statement which is used to prove other statements.

>Consider the division of positive integer by positive integer, say 58 by 9.

>Here, 9 is the divisor, 58 is the dividend, 6 is the quotient and 4 is the remainder. 

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Answer 2

If we have two positive integers suppose a and b than there is a unique integer exist q and r which satisfy the given equation :-

a = bq + r 

where 0 ≤ r ≤ b

Example :- Lets take two positive integer 58 by 9

Divisor is 9

Dividend is 58

Quotient is 6

Remainder is 4

By applying Euclid lemma

we get as,

58 = 9 × 6 + 4; 0 ≤ 4 ≤ 9.