Question

a positive integer a when divided by the smallest odd prime, leaves a reminder r. which of the following cannot be r :
a. 0
b. 1
c. 2
d. 3

Plz plz plz explain and answer.....​

Answer 1

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Answer 2

The value of r cannot be 3. hence option (d) is correct.

A positive integer a when divided by the smallest odd prime, leaves a remainder r.

Which of the following cannot be r ?

• a) 0
• b) 1
• c) 2
• d) 3

Before solving this question, we need to understand Euclid division lemma.

Euclid division lemma : If a number a is divided by any other number b, the quotient will be q and the remainder will be r, then, a = bq + r, where 0 ≤ r < b.

Now let's come to the point.

Here, we have to divide a positive integer ( say P ) by the smallest odd prime number.

We know, 3 is the smallest odd prime number.

From Euclid division Lemma, P = 3q + r  where, 0 ≤ r < 3.

It shows that r is less than 3. so the value of r can't be 3.

Therefore the value of r cannot be 3. hence option (d) is correct.

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