How many prime numbers are there in the following numbers 3,18,28,37,54,67,79,91,113,171,253,346

Options

A. 2
B. 3
C. 4
D. 5

Answer

To determine how many prime numbers are present in the list of numbers provided (3, 18, 28, 37, 54, 67, 79, 91, 113, 171, 253, 346), we will analyze each number one by one to check if it is prime.

### Step-by-step Solution:

1. **Identify the Numbers**: We have the following numbers: 3, 18, 28, 37, 54, 67, 79, 91, 113, 171, 253, 346.

2. **Definition of Prime Number**: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

3. **Check Each Number**:
- **3**: Divisible by 1 and 3. **Prime**.
- **18**: Divisible by 1, 2, 3, 6, 9, 18. **Not Prime**.
- **28**: Divisible by 1, 2, 4, 7, 14, 28. **Not Prime**.
- **37**: Divisible by 1 and 37. **Prime**.
- **54**: Divisible by 1, 2, 3, 6, 9, 18, 27, 54. **Not Prime**.
- **67**: Divisible by 1 and 67. **Prime**.
- **79**: Divisible by 1 and 79. **Prime**.
- **91**: Divisible by 1, 7, 13, 91. **Not Prime**.
- **113**: Divisible by 1 and 113. **Prime**.
- **171**: Divisible by 1, 3, 9, 19, 57, 171. **Not Prime**.
- **253**: Divisible by 1, 11, 23, 253. **Not Prime**.
- **346**: Divisible by 1, 2, 173, 346. **Not Prime**.

4. **Count the Prime Numbers**: The prime numbers we found are: 3, 37, 67, 79, and 113.

5. **Total Count**: There are 5 prime numbers in the list.

### Final Answer:
There are **5 prime numbers** in the given list.