A 6-digit number has digits as consecutive natural numbers. The number is always divisible by:
- 3
- 4
- 5
- 2
The Correct Option is A
Solution and Explanation
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.
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