Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.
(i) 81                     (ii) 128                    (iii) 135              (iv) 192 (v) 704

Explanation

To find the smallest number by which each of the following numbers must be divided to obtain a perfect cube, we will factor each number into its prime factors, group the factors into triplets, and identify any extra factors that prevent the number from being a perfect cube.

### Step-by-Step Solution:

**(i) For 81:**
1. **Factor 81:**
- 81 = 3 × 3 × 3 × 3 = \(3^4\)
2. **Group into triplets:**
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