Find the total number of factors of `2160` (excluding `1`)

Options

A. 40
B. 39
C. 41
D. 38

Answer

B

Explanation

We have,
`2160=2^(4)xx3^(3)xx5!`
The total number of divisors is same as the number of ways of selecting some or all out of four 2's three 3's and one 5's. The number of such ways is
`(4+1)(3+1)(1+1)-1=39`
`:.` Total number of factors = 39.