Consider `N=2^(2)3^(2)4^(2)6^(2)5^(2)` and give the answers of the following questions .
(i) Find the total number of divisible of N .
(ii) Find the total number of divisors divisible by 24
(iii) Find the total number of divisors divisible by 5.
(iv) Find the total number of divisors which are perfect square.
(v) Find the number of divisors which are perfect cube.

Explanation

`N=2^(2)3^(2)4^(2)6^(2)5^(2)=2^(2)3^(2)2^(4)2^(2)3^(2)5^(2)=2^(8)3^(4)5^(2)`
(i) Total divisors =(8+1)(4+1)(2+1)=135
(ii) N=(24) `(2^(6)3^(3)5^(2))`
Total divisors divisible by 24=(6+1)(3+1) (2+1)=84
(iii) `N=5(2^(8)3^(4)5^(1))` , total divisors divisible by 5 is (8+1)(4+1)(1+1)=90
(iv) `N=(2^(2))^(4)(3^(2))^(2)(5^(2))^(1)` , number of perfect square divisors =(4+1)(2+1)(1+1)=30
(v) `N=((2^(3))^(2). (3^(3))^(1))2^(2)3^(1)5^(2)`, number of perfect cube divisors =(2+1)(1+1)=6