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

Question

Accepted Answer

Let the six-digit number be represented by six consecutive natural numbers, such as 123456 or 456789.

#### Step 1: Sum of Digits in Arithmetic Progression
The sum of the digits of six consecutive natural numbers can be expressed as:  
$$
	ext{Sum} = n + (n+1) + (n+2) + (n+3) + (n+4) + (n+5)
$$  
Simplify:  
$$
	ext{Sum} = 6n + 15
$$

#### Step 2: Divisibility by 3
Since $$6n$$ is always divisible by 3 and $$15$$ is also divisible by 3, the entire sum $$6n + 15$$ is divisible by 3.

#### Step 3: Conclusion
The sum of the digits being divisible by 3 ensures that the number itself is divisible by 3, regardless of the starting digit $$n$$.

Thus, the number is always divisible by **3**.

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