When 14 is divided by 5, the remainder is 4. When 14 is divided by a positive integer n, the remainder is 2. For how many different values of n is this possible.

Question

Is listing it out the only way?

Answer 1

14/2 =7
14/3 = 4 2/3 yes
14/4 = 3 2/4 yes
14/5 = 2 4/5
14/6 = 2 2/6 yes
14/7 = 2
14/8 = 1 6/8
14/9 = 1 5/9
14/10 = 1 4/10
14/11 = 1 3/10
14/12 = 1 2/12 yes
the end
I got 3