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Question
Find the smallest number by which 8768 must be divided so that the quotient is a perfect cube.
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Solution
The prime factor of 8768 are
| 2 | 8768 |
| 2 | 4384 |
| 2 | 2192 |
| 2 | 1096 |
| 2 | 548 |
| 2 | 274 |
| 137 | 137 |
| 1 |
= 2 x 2 x 2 x 2 x 2 x 2 x 137
= (2 x 2 x 2) x (2 x 2 x 2) x 137
Clearly, 8768 must be divided by 137.
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