Question

explain the euclids division lemma

Answer 1

Heya!!

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Euclid's Division lemma:-Given two positive integers a and b,there exist two unique integers q and r satisfying a = bq+r ,0<=r<b.

Explanation:-
Let us take two positive integers,10 and 5.

Dividing 10 by 5,gives

10 = 5×2+0.(Dividend = Divisor × Quotient + Remainder)

Then if, a = 10(Dividend) and b= 5(Divisor), there exist two unique integers i.e the quotient (q) and remainder(r).

We know that,

Dividend =Divisor× Quotient +Remainder.
=>a =bq+r,0< or = r<b.

Remember: Remainder (r) will be always less than the Divisor.And Remainder can either become 0 or any positive integer.

Euclid's division lemma is nothing but form of writing our daily division process.

Hope it helps you.


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