Question
Which of the following are perfect cube? $456533$
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Answer
On factorising $456533$ into prime factors, we get $456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11$ Group the factors in triples of equal factors as: $456533 = \{7 \times 7 \times 7\} \times \{11 \times 11 \times 11\}$ It is evident that the prime factors of $456533$ can be grouped into triples of equal factors and no factor is left over. Therefore, $456533$ is a perfect cube.
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