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Question
Find the smallest number by which 10985 should be divided so that the quotient is a perfect cube
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Solution
| 5 | 10985 |
| 13 | 2197 |
| 13 | 169 |
| 13 | 13 |
| 1 |
We have 10985 = 5 × 13 × 13 × 13
= 5 × 13 × 13 × 13
Here we have a triplet of 13 and we are left over with 5.
If we divide 10985 by 5, the new number will be a perfect cube.
∴ The required number is 5.
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