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**Infinate Possibilities** Hi all!

I have this question:

Find all positive integers *n* (*n* will be called special)

such that if *n* divides a three digit number say ABC where A = hundreds, B = tens, C = ones. Then *n* also divides BCA and CAB.

So far I have worked out that 1 is special of course, so is 3 (factor test sum of digits will always be the same) and 9 as well as 111,222,333....999 and any number greater than 1000 as it will only divide into the 3 digit number 000.

I am told that there are two more such numbers *n* under 100. How do you find them? And please explan your reasoning. Thanks!