When 732 is divided by a positive integer x, the remainder is 12. How many values of x are there?

Number which fully divide by a positive integer x = number - remainder = 732 -12 = 720

720 is fully divide by positive integer x.

Factor of 720 = $$2^4 \times 3^2 \times 5

Total factor = (4 + 1).(2 + 1).(1 + 1) = 5.3.2 = 30

We combinations of these factors which are more than 12 and maximum 720 because remainder is 12.

Combination lees than 13 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12

Number of combination lees than 13 = 10

Number of values of x = 30 - 10 = 20