Which of the following equals the product of exactly two prime numbers?

Options

A. `11 cdot 6`
B. `13 cdot 22`
C. `14 cdot 23`
D. `13 cdot 23`

Answer

To determine which of the given options equals the product of exactly two prime numbers, we will evaluate each option step by step.

### Step 1: Analyze Option A - 11 × 6
- **Check if 6 is a prime number**: A prime number is only divisible by 1 and itself. The number 6 can be divided by 1, 2, 3, and 6. Therefore, 6 is not a prime number.
- **Conclusion**: Since one of the factors (6) is not prime, the product 11 × 6 is not the product of exactly two prime numbers.

### Step 2: Analyze Option B - 13 × 22
- **Check if 22 is a prime number**: The number 22 can be divided by 1, 2, 11, and 22. Thus, 22 is not a prime number.
- **Conclusion**: Since one of the factors (22) is not prime, the product 13 × 22 is not the product of exactly two prime numbers.

### Step 3: Analyze Option C - 14 × 23
- **Check if 14 is a prime number**: The number 14 can be divided by 1, 2, 7, and 14. Therefore, 14 is not a prime number.
- **Conclusion**: Since one of the factors (14) is not prime, the product 14 × 23 is not the product of exactly two prime numbers.

### Step 4: Analyze Option D - 13 × 23
- **Check if both 13 and 23 are prime numbers**:
- 13: The number 13 can only be divided by 1 and 13, making it a prime number.
- 23: The number 23 can only be divided by 1 and 23, making it a prime number.
- **Conclusion**: Both factors (13 and 23) are prime numbers. Therefore, the product 13 × 23 is indeed the product of exactly two prime numbers.

### Final Answer
The correct option that equals the product of exactly two prime numbers is **Option D: 13 × 23**.

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