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

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

(a) 19

(b) 20

(c) 18

(d) 16

Sol:

When 732 is divided by x remainder is 12. So, the number exactly divisible by x is 720.

The remainder is always less than the divisor, so 😡 > 12

Now, the factors of 720 which are more than 12 are possible values of x, i.e.

(15,16,18,20,24,30,36, 40,45, 48,60, 72, 80, 90, 120, 144, 180, 240, 360, 720).