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Question
Find the smallest number by which the following number must be divided to obtain a perfect cube.
192
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Solution
| 2 | 192 |
| 2 | 96 |
| 2 | 48 |
| 2 | 24 |
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
Here, one 3 is left, which is not in a triplet.
If we divide 192 by 3, then it will become a perfect cube.
Thus, 192 ÷ 3 = 64
= 2 × 2 × 2 × 2 × 2 × 2 is a perfect cube.
Hence, the smallest number by which 192 should be divided to make it a perfect cube is 3.
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