We call a number perfect if it is the sum of all its positive divisors, except itself. e.g. 28 is a perfect number because `28=1+2+4+7+14`. Which of the following numbers is a perfect number?

Options

A. 9
B. 6
C. 13
D. 10

Answer

To determine which of the given numbers is a perfect number, we need to find the sum of all positive divisors of each number, excluding the number itself, and see if that sum equals the number.

### Step-by-Step Solution:

1. **Identify the Numbers**: Let's assume the numbers we need to check are 9, 6, 13, and 10.

2. **Check the Number 9**:
- **Divisors of 9**: The positive divisors of 9 are 1, 3, and 9.
- **Sum of Divisors (excluding 9)**: 1 + 3 = 4.
- **Comparison**: 4 ≠ 9. So, 9 is not a perfect number.

3. **Check the Number 6**:
- **Divisors of 6**: The positive divisors of 6 are 1, 2, 3, and 6.
- **Sum of Divisors (excluding 6)**: 1 + 2 + 3 = 6.
- **Comparison**: 6 = 6. So, 6 is a perfect number.

4. **Check the Number 13**:
- **Divisors of 13**: The positive divisors of 13 are 1 and 13.
- **Sum of Divisors (excluding 13)**: 1.
- **Comparison**: 1 ≠ 13. So, 13 is not a perfect number.

5. **Check the Number 10**:
- **Divisors of 10**: The positive divisors of 10 are 1, 2, 5, and 10.
- **Sum of Divisors (excluding 10)**: 1 + 2 + 5 = 8.
- **Comparison**: 8 ≠ 10. So, 10 is not a perfect number.

### Conclusion:
After checking all the numbers, we find that the only perfect number among the options is **6**.