Question

explain euclids division lemma

Answer 1

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.
We can write the result in following form
Dividend = Divisor X quotient + Remainder 
58 = 9 x 6 + 4; 0 ≤ 4 ≤ 9 
For each pair of positive integers a and b, we can find unique integers q and r satisfying the relation 
a = bq + r , 0 ≤ r ≤ b.