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Question
Find the smallest number by which the following number must be divided to obtain a perfect cube.
135
Solution
| 3 | 135 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
135 = 3 × 3 × 3 × 5
Here, one 5 is left, which is not in a triplet.
If we divide 135 by 5, then it will become a perfect cube.
Thus, 135 ÷ 5 = 27
= 3 × 3 × 3 is a perfect cube.
Hence, the smallest number by which 135 should be divided to make it a perfect cube is 5.
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