Question

Which of the following numbers are not perfect cubes?

• A. $216$
• B. $128$
• C. $1000$
• D. $100$

Answer 1

The correct option is D $100$

We have 216 = 2 × 2 × 2 × 3 × 3 × 3

Grouping the prime factors of 216 into triples,

no factor is left over.

216 is a perfect cube.

We have 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

Grouping the prime factors of 128 into triples, we are left over with 2 as ungrouped factor.

∴ 128 is not a perfect cube.

We have 1000 = 2 × 2 × 2 × 5 × 5 × 5

Grouping the prime factors of 1000 into triples, we are not left over with any factor.

∴ 1000 is a perfect cube.

We have 100 = 2 × 2 × 5 ×5

Grouping the prime factors into triples, we do not get any triples. Factors 2 × 2 and 5 × 5 are not in triple

∴ 100 is not a perfect cube.