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Product of all the even divisors of N = ...

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

A

`2^(20)*5^(20)`

B

`2^(24)*5^(24)`

C

`64*10^(18)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(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)`
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