Question

SUBJECT-MATHIEMATICS
CLASS-101
For any integer a and 3, there exists unique integers q and r such that a=3q+r. Find the
possible values of r.
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Answer 1

• r is equal or greater than 0 but less than mod r

Answer 2

Euclid’s division Lemma:

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 :

a = 3q+r

In this question,

b = 3

The values 'r’ can take 0 ≤ r < 3.

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