Product of all the even divisors of `N = 1000`, is

Options

A. `2^(20)*5^(20)`
B. `2^(24)*5^(24)`
C. `64*10^(18)`
D. None of these

Answer

B

Explanation

`(b)` `1000=2^(3)*5^(3)`
Number of divisors `=16` which are
`(2^(0)+2^(1)+2^(2)+2^(3))(5^(0)+5^(1)+5^(2)+5^(3))`
Product of all the `16` divisors is
`=(5^(6))(5^(6))(5^(6))(5^(6))(2^(6))(2^(6))(2^(6))(2^(6))`
`=2^(24)*5^(24)`