Which of the following statements is correct ?

Question

Accepted Answer

Option 4 is the correct answer: "1 is neither prime nor a composite number."

### Explanation for Option 4:

1. **Definition of Prime Numbers**: A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. Since 1 is not greater than 1, it does not meet the basic criterion to be considered a prime number.

2. **Definition of Composite Numbers**: A composite number is a natural number greater than 1 that has more than two positive divisors. Since 1 is not greater than 1 and has only one positive divisor (itself), it cannot be classified as a composite number.

3. **Mathematical Consensus**: In mathematics, 1 is considered a unique number that does not fit into the categories of prime or composite numbers. This is a widely accepted convention in number theory.

### Explanation for Why Other Options are Incorrect:

1. **Option 1: "1 is a prime number"** - This is incorrect because, as stated earlier, a prime number must be greater than 1. Since 1 does not satisfy this condition, it cannot be classified as a prime number.

2. **Option 2: "1 is a composite number"** - This is incorrect because a composite number must have more than two positive divisors and must be greater than 1. The number 1 only has one positive divisor (itself) and is not greater than 1, so it cannot be considered composite.

3. **Option 3: "1 is both, a prime and a composite number"** - This is incorrect because 1 does not meet the criteria for being either a prime or a composite number, as explained above. Therefore, it cannot be both.

In conclusion, Option 4 is the correct answer because 1 does not meet the criteria to be classified as either a prime or a composite number.