Question

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

Answer 1

Given:

732 is divided by a positive integer x, the remainder is 12

To Find:

Number of values of x.

Solution:

Given 732 is divided by x and we get 12 as reminder.

In order to get 12 as reminder the divisor should be greater than 12.

Therefore, x > 12 .

Now

• 732 = x n + 12
• x n  = 720

Now we need to find factors of 720, such that x > 12.

• 720 = 9 x 4x 5 x 2 x 2   = $2^{4}$ x 3² x 5

Combinations of these numbers which are greater than 12 ,

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

The number of values of x are 20