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Question
Which of the following is perfect cube?
3087
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Solution
On factorising 3087 into prime factors, we get:
\[3087 = 3 \times 3 \times 7 \times 7 \times 7\]
Group the factors in triples of equal factors as:
\[3087 = 3 \times 3 \times \left\{ 7 \times 7 \times 7 \right\}\]
It is evident that the prime factors of 3087 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 243 is a not perfect cube.
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