One' is

Options

A. prime number
B. composite number
C. Both (a) and (b)
D. Neither (a) nor (b)

Answer

To determine whether the number 1 is a prime number, composite number, or neither, we can follow these steps:

### Step 1: Understand the definitions
- **Prime Number**: A prime number is defined as a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
- **Composite Number**: A composite number is a natural number greater than 1 that has more than two positive divisors.

### Step 2: Analyze the number 1
- The number 1 has only one positive divisor, which is itself (1).

### Step 3: Compare with definitions
- Since a prime number must have exactly two distinct positive divisors and a composite number must have more than two, we can see that:
- 1 does not meet the criteria for being a prime number (it has only one divisor).
- 1 does not meet the criteria for being a composite number (it does not have more than two divisors).

### Step 4: Conclusion
- Therefore, the number 1 is neither a prime number nor a composite number.

### Final Answer
- The correct classification for the number 1 is that it is **neither prime nor composite**.

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