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Question
Find the smallest number by which the following number must be divided to obtain a perfect cube.
704
Solution
| 2 | 704 |
| 2 | 352 |
| 2 | 176 |
| 2 | 88 |
| 2 | 44 |
| 2 | 22 |
| 11 | 11 |
| 1 |
704 = 2 × 2 × 2 × 2 × 2 × 2 × 11
Here, one 11 is left, which is not a triplet.
If we divide 704 by 11, then it will become a perfect cube.
Thus, 704 ÷ 11
= 64
= 2 × 2 × 2 × 2 × 2 × 2 is a perfect cube.
Hence, the smallest number by which 704 should be divided to make it a perfect cube is 11.
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