Question

TH110 UU
5. For the any positive integers a and 3, there exist unique integers q and r such that a = 3q+r,
wherer r <_____
(2, 3, 4)​

Answer 1

Answer:

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≤r<3.

Hence, the possible values 'r’ can take is 0,1,2.