NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Fill in the Blanks
Question 147

Question. 147

If the sum of the digits in a number is a ____ of 3, then the number is divisible by 3.

Answer:

multiple

Detailed Answer with Explanation:

Divisibility rule for 3 (easy steps)

  1. Take the number and add all its digits. Call this sum S.
  2. If S is a multiple of 3, then the original number is divisible by 3.

Why this works (in small steps)

Let the number be \(N\) and the sum of its digits be \(S\).

Check if \(S\) can be written as:

\(S = 3 \times k\)   for some whole number \(k\).

If yes, then:

\(N\) is divisible by \(3\).

Example 1

\(N = 123\)

Add digits: \(1 + 2 + 3\)

\(= 6\)

Check multiple of 3: \(6 = 3 \times 2\) → yes

So, \(123\) is divisible by \(3\).

Example 2 (not divisible)

\(N = 124\)

Add digits: \(1 + 2 + 4\)

\(= 7\)

\(7\) is not a multiple of \(3\).

So, \(124\) is not divisible by \(3\).

Conclusion: The blank is multiple.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 1: Number System – Fill in the Blanks | Detailed Answers