Question
Which of the following are perfect cube$?$
$243$
$243$
✓
Answer
On factorising $243$ into prime factors, we get
$243 = 3 × 3 × 3 × 3 × 3$
Group the factors in triples of equal factors as:
$243 = \{3 × 3 × 3\} × 3 × 3$
It is evident that the prime factors of $243$ can be grouped into triples of equal factors and no factor is left over.
Therefore, $243$ is a perfect cube.
$243 = 3 × 3 × 3 × 3 × 3$
Group the factors in triples of equal factors as:
$243 = \{3 × 3 × 3\} × 3 × 3$
It is evident that the prime factors of $243$ can be grouped into triples of equal factors and no factor is left over.
Therefore, $243$ is a perfect cube.
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