Question

plz explain me Euclid's division lemma

Answer 1

Euclid's division lemma states that" given positive integers 'a' and 'b' the exists a unique pair of integers'q' and 'r' satisfying a=bq+r. and 0≤r<b.

let us take an example of the numbers 7 and 2.
here, a=7 and b=2
we can write it as,
7=2*0+7
7=2*1+5
7=2*2+3
7=2*3+1

but according to the condition 0≤r<b,
only 7=2*3+1 is possible.
so if a and b are fixed, then q and r are also fixed.

hope it helps

Answer 2

lemma is a restatement of the long division process ...
consider the division of one positive integer by another say 58 by 9.
the division can be carried out as follows
while carried out the division , we had to think of about the largest multiple of 9 which does not exceed 58 ....so that after subtraction the remainder 4 is less than the divisor 9.
the result of this division is that we get 2 integers namely 6 which is called the quotient
and 4 which is called the remainder....
we can write the result in the following form.
58= 9×6+4
hope this helps you.....