Question

Which of the following numbers are perfect cubes?

• A. $108$
• B. $343$
• C. $243$
• D. $5,324$

Answer 1

Answer: (B)

$343$

We know, a perfect cube has multiples of $3$ as powers of prime factors.

Prime factorisation of:

A) $108=2\times 2\times 3\times 3\times 3=2^2\times 3^3$, which is not a perfect cube.

B) $343=7\times 7\times 7=3^3$, which is a perfect cube.

C) $243=3\times 3\times 3\times 3\times 3=3^5$, which is not a perfect cube.

D) $5324=2\times 2\times 11\times 11\times 11=2^2\times {11}^3$, which is not a perfect cube.

Therefore only $343$ is a perfect cube.

Hence, option $B$ is correct.