nil_986 wrote:Is 12**66* divisible by 564 ? {Here * can be any digit but not the same }

Dear nil_986,
I would like to help you, but this question is somewhat unclear. First of all, it's not in GMAT question format at all, and in fact, the nature of what it is asking, I believe, well beyond the GMAT.

The * digits can't be the same as each other, but it's not clear whether they can be 1, 2, or 6, the digits that already appear. If they can repeat those digits, there are 720 possible numbers. If they can't repeat them, there are 210 possible numbers.

Now, given that wide range of possible numbers, it's hard to know what is meant by the question. Obviously, not all possible numbers would be divisible by 564. Is the challenge to find one number that is divisible by 564?

564 = 2*2*3*47, which is the prime factorization of 564. See this post for more on prime factorizations:
https://magoosh.com/gmat/2012/gmat-math-factors/
Any number divisible by 564 would have to be divisible by all those factors.

If you can clarify the question, I would be happy to help you further.
Mike