Pick a two digit number with distinct digits. Now, reverse the digits. Subtract the smaller number from the larger number. The difference thus obtained is always divisible by
Let the two digit number be ab.
its reverse will be 10b+a
10a+b - (10b+a) = 9a−9b
We could also have
10b+a - (10a+b) = 9b−9a
which would yield 9(a−b) or 9(b−a).
In both the cases, the number thus obtained will be a multiple of 9 and thus will be divisible by 9. Since 3 is a factor of 9, the number obtained will be divisible by 3 as well.