Question

Which of the following numbers is perfect cube?

• A. $256$
• B. $625$
• C. $343$
• D. $243$

Answer 1

Answer: (C)

The correct option is C $343$

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

Now, prime factorisation of:

A) $625=5\times 5\times 5\times 5$ $=5^4$, which is not a perfect cube.

B) $256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$ $=2^8$, which is not a perfect cube.

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

D) $243=3\times 3\times 3\times 3\times 3$ $=3^5$, which is cot a perfect cube.

Hence, option $C$ is correct.