Which of the following is a prime number ?

Options

A. 143
B. 131
C. 147
D. 161

Answer

To determine which of the given options is a prime number, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Prime Numbers**:
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. This means it cannot be formed by multiplying two smaller natural numbers.

2. **Evaluate Option 1: 143**:
- Check if 143 can be divided by any number other than 1 and 143.
- When we divide 143 by 13, we get:
\[ 143 \div 13 = 11 \]
- Since 143 can be divided by 13, it is not a prime number.

3. **Evaluate Option 2: 131**:
- Check if 131 can be divided by any number other than 1 and 131.
- The only divisors of 131 are 1 and 131 itself.
- Therefore, 131 is a prime number.

4. **Evaluate Option 3: 147**:
- Check if 147 can be divided by any number other than 1 and 147.
- The sum of the digits of 147 is \(1 + 4 + 7 = 12\), which is divisible by 3.
- When we divide 147 by 3, we get:
\[ 147 \div 3 = 49 \]
- Since 147 can be divided by 3, it is not a prime number.

5. **Evaluate Option 4: 161**:
- Check if 161 can be divided by any number other than 1 and 161.
- When we divide 161 by 7, we get:
\[ 161 \div 7 = 23 \]
- Since 161 can be divided by 7, it is not a prime number.

### Conclusion:
After evaluating all options, the only number that is a prime number is **Option 2: 131**.