Find the number of divisors of the number `N=2^3 .3^5 .5^7 .7^9` which are perfect squares.

Explanation

To find the number of divisors of the number \( N = 2^3 \cdot 3^5 \cdot 5^7 \cdot 7^9 \) that are perfect squares, we will follow these steps:

### Step 1: Understand the condition for perfect squares
A divisor is a perfect square if all the exponents in its prime factorization are even numbers.

### Step 2: Identify the prime factorization of \( N \)
The prime factorization of \( N \) is given as:
- \( 2^3 \)
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