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Question
Find the smallest number by which the following number must be multiplied to obtain a perfect cube.
243
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Solution
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
243 = 3 × 3 × 3 × 3 × 3
∴ 243 is not a perfect cube.
Here, two 3s are left that are not in a triplet. To make 243 a cube, one more 3 is required.
In that case, 243 × 3 = 3 × 3 × 3 × 3 × 3 × 3 = 729 is a perfect cube.
Hence, the smallest natural number by which 243 should be multiplied to make it a perfect cube is 3.
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