Question

The total numer of all proper factors of 75600 is

• A. 120
• B. 119
• C. 118
• D. None of these

Answer 1

The correct option is C 118

We have, 75600 = $2^4.3^3.5^2.7$
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
But this includes the given number itself. Therefore, the required number of proper factors is 118.