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Question
Find the smallest number by which 26244 may be divided so that the quotient is a perfect cube.
Solution
The prime factors of 26244 are
| 2 | 26244 |
| 2 | 13122 |
| 3 | 6561 |
| 3 | 2187 |
| 3 | 729 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
= 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3
= (3 x 3 x 3) x (3 x 3 x 3) x 3 x 3 x 2 x 2
Clearly, 26244 must be divided by
3 x 3 x 2 x 2 = 36
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