Question

Which of the following numbers is a perfect cube?

Options

• 243

• 216

• 392

• 8640

Answer 1

216

Explanation:

a. We have, 243

Resolving 243 into prime factors, we have

243 = 3 × 3 × 3 × 3 × 3

Grouping the factors in triplets of equal factors, we get

243 = (3 × 3 × 3) × 3 × 3

Clearly, in grouping, the factors in triplets of equal factors, we are left with two factors 3 × 3.

Therefore, 243 is not a perfect cube.

b. We have, 216

Resolving 216 into prime factors, we have

216 = 2 × 2 × 2 × 3 × 3 × 3

Grouping the factors in triplets of equal factors, we get

216 = (2 × 2 × 2) × (3 × 3 × 3)

Clearly, in grouping, the factors of triplets of equal factors, no factor is left over.

So, 216 is a perfect cube.

c. We have, 392

Resolving 392 into prime factors, we get

392 = 2 × 2 × 2 × 7 × 7

Grouping the factors in triplets of equal factors, we get

392 = (2 × 2 × 2) × 7 × 7

Clearly, in grouping, the factors in triplets of equal factors, we are left with two factors 7 × 7.

Therefore, 392 is not a perfect cube.

d. We have, 8640

Resolving 8640 into prime factors, we get

8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5

Grouping the factors in triplets of equal factors, we get

8640 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × 5

Clearly, in grouping, the factors in triplets of equal factors, we are left with one factor 5.

Therefore, 8640 in not a perfect cube.

After solving, it is clear that 216 is correct.