Which of the following is a prime number?

Question

Accepted Answer

Option 3, which is 149, is the correct answer because 149 is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Let's examine why 149 is a prime number and why the other options are not.

1. **149 (Option 3):**  
   - 149 is a prime number because it cannot be divided evenly by any other numbers except 1 and 149. When you test divisibility by prime numbers less than the square root of 149 (which is approximately 12.2), you find that 149 is not divisible by 2, 3, 5, 7, or 11. Therefore, 149 has no divisors other than 1 and itself, confirming it is a prime number.

2. **117 (Option 1):**  
   - 117 is not a prime number because it can be divided by numbers other than 1 and itself. Specifically, 117 is divisible by 3 (117 ÷ 3 = 39) and 9 (117 ÷ 9 = 13), among others. Since it has divisors other than 1 and 117, it is not a prime number.

3. **147 (Option 2):**  
   - 147 is not a prime number because it can be divided by numbers other than 1 and itself. For example, 147 is divisible by 3 (147 ÷ 3 = 49) and 7 (147 ÷ 7 = 21). These additional divisors mean that 147 is not a prime number.

4. **159 (Option 4):**  
   - 159 is not a prime number because it can be divided by numbers other than 1 and itself. It is divisible by 3 (159 ÷ 3 = 53), which means it has divisors other than 1 and 159, confirming it is not a prime number.

In conclusion, Option 3 (149) is the only number among the given options that meets the criteria of a prime number, as it has no divisors other than 1 and itself.