Which of the following is a perfect number?

Options

A. 6
B. 12
C. 24
D. 8

Answer

To determine which of the following numbers is a perfect number, we will check each option one by one. A perfect number is defined as a number that is equal to the sum of its proper divisors (excluding itself).

### Step-by-Step Solution:

1. **Check Option 1: 6**
- **Find the divisors of 6:** The divisors are 1, 2, and 3.
- **Calculate the sum of the divisors:**
\[ 1 + 2 + 3 = 6 \]
- **Comparison:** Since the sum of the divisors (6) is equal to the number itself (6), 6 is a perfect number.

2. **Check Option 2: 12**
- **Find the divisors of 12:** The divisors are 1, 2, 3, 4, and 6.
- **Calculate the sum of the divisors:**
\[ 1 + 2 + 3 + 4 + 6 = 16 \]
- **Comparison:** The sum of the divisors (16) is not equal to the number itself (12), so 12 is not a perfect number.

3. **Check Option 3: 24**
- **Find the divisors of 24:** The divisors are 1, 2, 3, 4, 6, 8, and 12.
- **Calculate the sum of the divisors:**
\[ 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36 \]
- **Comparison:** The sum of the divisors (36) is not equal to the number itself (24), so 24 is not a perfect number.

4. **Check Option 4: 8**
- **Find the divisors of 8:** The divisors are 1, 2, and 4.
- **Calculate the sum of the divisors:**
\[ 1 + 2 + 4 = 7 \]
- **Comparison:** The sum of the divisors (7) is not equal to the number itself (8), so 8 is not a perfect number.

### Conclusion:
The only perfect number among the options is **Option 1: 6**.

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