Which of the following is a prime number ?

Options

A. 117
B. 171
C. 179
D. none of these

Answer

To determine which of the given numbers is a prime number, we will follow these steps:

### Step 1: Understand what a prime number is.
A prime number is defined as a number that has exactly two distinct positive divisors: 1 and itself.

### Step 2: Analyze the first number, 117.
- We need to check the factors of 117.
- 117 can be factored into 3 and 39 (since 117 = 3 × 39).
- Since 117 has factors other than 1 and itself (it can be divided by 3 and 39), it is **not a prime number**.

### Step 3: Analyze the second number, 171.
- Now, let's check the factors of 171.
- 171 can be factored into 3 and 57 (since 171 = 3 × 57).
- Again, since 171 has factors other than 1 and itself (it can be divided by 3 and 57), it is **not a prime number**.

### Step 4: Analyze the third number, 179.
- Finally, we check the factors of 179.
- The only factors of 179 are 1 and 179 itself (since it cannot be divided evenly by any other number).
- Since 179 has no other factors, it is **a prime number**.

### Conclusion:
From the analysis, the only prime number among the given options is **179**.

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