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Combination of n Different Things Taken One or More at a Time

The number of...

Question

The number of proper divisors of $2160$ is

40

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39

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38

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18

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Solution

The correct option is C $38$
$2160 = 2^{4} . 3^{3} . 5^{1}$
Proper factors $= (4 + 1) (3 + 1) (1 + 1) - 2 = 38$

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N = 2^{p} . 3^{q} . 5^{r}

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