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

To solve the problem step by step, we will first express \( N \) in its prime factorization form and then use the properties of divisors to answer each part of the question.

### Step 1: Prime Factorization of \( N \)

Given:
\[ N = 2^2 \cdot 3^2 \cdot 4^2 \cdot 6^2 \cdot 5^2 \]

We can express \( 4 \) and \( 6 \) in terms of their prime factors:
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