C# return multiples of a number in a number and the remainder?

C# return multiples of a number in a number and the remainder?

I want to find all multiples of 3 given a certain number, and also find
the remainder.
So for example:
Given the number 10 : multiples of 3 = {3;6;9} + remainder = 1
Given the number 11 : multiples of 3 = {3;6;9} + remainder = 2
The algorithm I have so far (but not code) goes like this:
Check if X is a multiple of 3 - Yes - return multiples (no remainder);
No? is x-1 a multiple of 3 - Yes - return multiples (1 remainder);
No? is x-2 a multiple of 3 - Yes - return multples (2 remainder);
Is there a better way to do this, using less code?
Edit: 2 more things, I'm only looking for 3 - so this could be a const.
Also any number smaller than 3: 2, 1 and 0 - I don't mind having
additional logic for that.