The answer choices are factors of x. Let's find the minimum value that x can have since the factor must be for any value of x.


Basically, there can be 6 such integers that can be constructed. To find the minimum sum of these integers, let's assume least values that a, b, and c can have: a=1, b=2, and c=3.

Next step is to arrange these digits, construct integers, and add to produce x.
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1

Add up. x = 1332. This must be divisible by 3. Try dividing by 6, you get 222 as quotient. So, 222 must also divide x completely. We are looking for the largest divisor among the answer choices. Hence, E is the correct answer.

Why just 1,2,3. The distinct non-zero digits are 1,2,3,4,5,6,7,8 & 9.

If we consider the non-zero distinct numbers a,b,c - total 6 3-digit numbers can be constructed.
abc
acb
bca
bac
cba
cab

We can write abc as 100a + 10b +c. If we write every number in this format and add all these 6 numbers we get 200(a+b+c) + 20(a+b+c) + 2(a+b+c).
Now we take (a+b+c) as common and rewrite it as (a+b+c)(200 + 20 + 2) i.e (a+b+c)(222).
Hence it is conspicuous that 222 is the largest number we can divide with. So the ans is E