If is a 3-digit number, then the number

is always divisible by

We have been given a 3-digit number, and another number,

Here, take one of the numbers from the given additions of n, say, .

The cyclic permutation of this number can be written as,

And this we know, can be written as

So,

…(i)

Now take another set of numbers, .

These are also cyclic permutation of .

Add these cyclic permutation, we get

And this in turn can be written as,

So,

…(ii)

Adding equations (i) and (ii), we get

⇒ n = 222 (a + b + c)

⇒ n = 6 × 37 × (a + b + c)

Notice that, the number is always divisible by 6.