Question
When 732 is divided by a positive integer x, the
remainder is 12. How many values of x are there?Solution
When 732 is divided by a positive integer x, the remainder is 12. So, 732 – 12 = 720 So 720 will be completely divisible by x 720 = 2 × 3 × 5 Total number of factors of 720 = (4 + 1) × (2 + 1) × (1 + 1) = 5 × 3 × 2 = 30 Number of factors 12 or less than 12 are (10) = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 So x cannot have these values because x is greater than 12 So, we can say that there are 30 - 10 = 20 possible values of x
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