Factors Of 3-digit Numbers
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!