Question

Which of the following numbers is not a perfect cube?

• A. $512$
• B. $2917$
• C. $2197$
• D. $343$

Answer 1

The correct option is B

$2917$

Explanation for the correct answer:

Option B : $2917$

Perfect cube is the product of three same integers.

Prime factorization of $2917$:

$2917=1\times 2917$

$2917$ is not product of three same integers.

Hence, $2917$ it is not a perfect cube.

So, Option B is the correct answer.

Explanation for the in-correct answer:

Option A : $512$

Prime factorization of $512$:

$512=8\times 8\times 8$

$512$ is the product of three same integers.

Hence, $512$ is a perfect cube.

So, Option A is not the correct answer.

Option C: $2197$

Prime factorization of $2197$:

$2197=13\times 13\times 13$

$2197$ is the product of three same integers.

Hence, $2197$ is a perfect cube.

So, Option C is not the correct answer.

Option D: $343$

Prime factorization of $343$:

$343=7\times 7\times 7$

Since,$343$ is the product of three same integers.

Hence it is a perfect cube.

Hence, $343$ is a perfect cube.

So, Option D is not the correct answer.

Hence, the correct option is option $B$.