Question

A 6-digit number has digits as consecutive natural numbers. The number is always divisible by:

• A. 3
• B. 4
• C. 5
• D. 2

Answer 1

The Correct Option is A

A 6-digit number formed by consecutive natural numbers can be represented as: \( n, n+1, n+2, n+3, n+4, n+5 \). The sum of these digits will be:

\[ S = n + (n+1) + (n+2) + (n+3) + (n+4) + (n+5) \]

\[ S = 6n + 15 \]

This expression \( 6n + 15 \) is always divisible by 3 because:

- Any integer \( n \) when multiplied by 6 results in a number divisible by 3, as 6 itself is divisible by 3.

- The constant 15 is divisible by 3.

Therefore, \( 6n + 15 \) is divisible by 3, making the original number always divisible by 3.