NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - True or False Questions

Question 83

Why this is true (step by step):

1. Take any number with 4 or more digits. Write it as two parts:
   (all the digits except the last three) and (the last three digits).
2. Suppose the number is (N). Then we can write:
   (N = \text{(thousands part)} \times 1000 + \text{(last three-digit number)}\).
3. Note that (1000 = 8 \times 125\). So (1000\) is divisible by (8\).
4. This means (\text{(thousands part)} \times 1000\) is also divisible by (8\).
5. A sum is divisible by (8) only if the non-divisible part is also divisible by (8). Here, the only part we need to check is the last three-digit number.
6. Therefore, (N) is divisible by (8\) if and only if its last three digits form a number divisible by (8\).

Quick example:
Consider (54{,}328\). Last three digits: (328\). Since (328 = 8 \times 41\), (328\) is divisible by (8\). So (54{,}328\) is divisible by (8\).