Question

for any integer a and 3 there exists unique integer q and r such that a=3q+r.find the possible value or 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.


SOLUTION :
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.

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

Sol : Using Euclid's division lemma a = bq +r and 0 ≤ r < b. Here a = 3q + r 0 ≤ r < 3 ∴ Correct option is 'a'.