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Question
Which is the smallest number that must be multiplied to 77175 to make it a perfect cube?
Solution
The prime factor of 77175 are
| 3 | 77175 |
| 3 | 25725 |
| 5 | 8575 |
| 5 | 1715 |
| 7 | 343 |
| 7 | 49 |
| 7 | 7 |
| 1 |
= 3 x 3 x 5 x 5 x 7 x 7 x 7
= (7 x 7 x 7) x 3 x 3 x 5 x 5
Clearly, 77175 must be multiplied by 3 x 5
= 15
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