Question 71

When 200 is divided by a positive integer x , the remainder is 8. How many values of x are there?

Solution

When 200 is divided by a positive integer x , the remainder is 8.

For completely divisible by x, number = 200 - 8 = 192

Factor of 192 = $$2^6 \times 3^1$$

Total number = (6 + 1)(1 + 2) = 14

Number which are less then 9 = 1, 2, 3, 4, 6, 8

Total number of values = 14 -6 = 8

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