Question

For any integers $a$ and $3$, there exists unique integers $q$ and $r$ such that $a=3q+r$. Find the possible value of $r$.

Answer 1

Euclid’s division Lemma:

It tells us about the divisibility of integers. It states that any positive integer ‘a’ can be divided by any other positive integer ‘ b’ in such a way that it leaves a remainder ‘r’.

Euclid's division Lemma states that for any two positive integers ‘a’ and ‘b’ there exist two unique whole numbers ‘q’ and ‘r’ such that , a = bq + r, where 0≤ r < b.

Here, a= Dividend, b= Divisor, q= quotient and r = Remainder.

Given : $a=3q+r$
In this question ,
$b=3$
The values 'r’ can take $0\le r<3.$
Hence, the possible values 'r’ can take is $0,1,2.$