Find the total number of positive integral solutions for `(x ,y ,z)` such that `x y z=24.` Also find out the total number of integral solutions.

Explanation

To find the total number of positive integral solutions for the equation \(xyz = 24\), we can follow these steps:

### Step 1: Prime Factorization of 24
First, we need to express 24 in terms of its prime factors:
\[ 24 = 2^3 \times 3^1 \]

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