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Question

The total number of all proper factors of 75600 (including number 1) is

A
120
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B
119
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C
118
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D
None of these
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Solution

The correct option is B 119
We have, 75600 = 24.33.52.7
The total number of ways of selecting some or all out of four 2's, three 3's, two 5's and one 7's is
(4 + 1)(3 + 1)(2 + 1)(1 + 1) - 1 = 119
Therefore, the required number of proper factors is 119.

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