When a two digit number divides 265, the remainder is 5. The number of such two digit numbers is

Correct Answer: 6

Solution

Since the remainder is 5, the divisor must divide $$265 - 5 = 260$$ exactly and be greater than 5. Since $$260 = 2^2 \times 5 \times 13$$, its two digit divisors are 10, 13, 20, 26, 52 and 65, giving 6 such numbers.

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