Which of the following numbers is a perfect cube?

Options

A. 141
B. 294
C. 216
D. 496

Answer

To determine which of the given numbers is a perfect cube, we will factor each number and check if the factors can be grouped into sets of three.

### Step-by-Step Solution:

1. **Check Option A: 141**
- Factor 141:
- 141 ÷ 3 = 47
- 141 = 3 × 47
- Since 47 is a prime number, we cannot group the factors into sets of three.
- **Conclusion**: 141 is not a perfect cube.

2. **Check Option B: 294**
- Factor 294:
- 294 ÷ 2 = 147
- 147 ÷ 3 = 49
- 49 = 7 × 7
- Therefore, the complete factorization is:
- 294 = 2 × 3 × 7 × 7
- We do not have any groups of three identical factors.
- **Conclusion**: 294 is not a perfect cube.

3. **Check Option C: 216**
- Factor 216:
- 216 ÷ 6 = 36
- 36 ÷ 6 = 6
- 6 = 6 × 1
- Alternatively, we can factor it as:
- 216 = 6 × 6 × 6
- This shows that all factors are identical (6).
- **Conclusion**: 216 is a perfect cube (6³).

4. **Check Option D: 496**
- Factor 496:
- 496 ÷ 2 = 248
- 248 ÷ 2 = 124
- 124 ÷ 2 = 62
- 62 ÷ 2 = 31
- Therefore, the complete factorization is:
- 496 = 2 × 2 × 2 × 2 × 31
- We do not have any groups of three identical factors.
- **Conclusion**: 496 is not a perfect cube.

### Final Answer:
The only number that is a perfect cube among the options is **Option C: 216**.

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