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प्रश्न
By which smallest number must the following number be divided so that the quotient is a perfect cube?
107811
उत्तर
On factorising 107811 into prime factors, we get:
\[107811 = 3 \times 3 \times 3 \times 3 \times 11 \times 11 \times 11\]
On group the factors in triples of equal factors, we get:
\[107811 = \left\{ 3 \times 3 \times 3 \right\} \times 3 \times \left\{ 11 \times 11 \times 11 \right\}\]
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