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Find the smallest number by which 10985 should be divided so that the quotient is a perfect cube.

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Find the smallest number by which 10985 should be divided so that the quotient is a perfect cube.

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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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