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 first need to understand the definition of a perfect number. A perfect number is a positive integer that is equal to the sum of its proper divisors (factors), excluding itself.

Let's analyze the options step by step.

### Step 1: Identify the options
Let's assume the options are:
- A) 6
- B) 12
- C) 8
- D) 28

### Step 2: Check each option for perfect number status

**Option A: 6**
1. Find the factors of 6: 1, 2, 3, 6.
2. Exclude 6 and sum the proper divisors: 1 + 2 + 3 = 6.
3. Since the sum of the proper divisors equals 6, **6 is a perfect number**.

**Option B: 12**
1. Find the factors of 12: 1, 2, 3, 4, 6, 12.
2. Exclude 12 and sum the proper divisors: 1 + 2 + 3 + 4 + 6 = 16.
3. Since the sum of the proper divisors (16) does not equal 12, **12 is not a perfect number**.

**Option C: 8**
1. Find the factors of 8: 1, 2, 4, 8.
2. Exclude 8 and sum the proper divisors: 1 + 2 + 4 = 7.
3. Since the sum of the proper divisors (7) does not equal 8, **8 is not a perfect number**.

**Option D: 28**
1. Find the factors of 28: 1, 2, 4, 7, 14, 28.
2. Exclude 28 and sum the proper divisors: 1 + 2 + 4 + 7 + 14 = 28.
3. Since the sum of the proper divisors equals 28, **28 is a perfect number**.

### Conclusion
From the analysis, we find that both 6 and 28 are perfect numbers. However, if we are to select only one option, the first option (6) is the simplest and the first perfect number.

### Final Answer
**The perfect number from the options is 6.**