15 divided by posative integer k, the remainder is 3 how many different values of k are true

Question

trying to find how many different values of k are true when 15 is divided by k which is a posative integer

Answer 1

15/k=n+3/k is another way of expressing the problem, where n is any positive integer.

So, 15=nk+3, nk=12, n=12/k. k could be any factor of 12, that is, 2, 3, 4, 6, 12. But this is not the answer because, for example, 15/2 has a remainder of 1; neither could k be 3 because the remainder would be 0. So if we exclude 2 and 3, we are left with k=4, 6 or 12. So there are three possible values for k.