Question

The natural number 1 is :

• A. a prime number.
• B. a composite number.
• C. prime as well as composite.
• D. neither prime nor composite.

Hint:

2 is the smallest prime number and the only even prime number. 4 is the smallest composite number.

Answer 1

The Correct Option is D

To determine whether the natural number 1 is a prime number, a composite number, or neither, we need to understand the definitions of prime and composite numbers:

• Prime Number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
• Composite Number: A composite number is a natural number greater than 1 that has more than two positive divisors.

Let's analyze the number 1 based on these definitions:

1. The number 1 is not greater than 1, which immediately excludes it from being a prime number since prime numbers must be greater than 1.
2. The number 1 does not have more than two positive divisors. In fact, it only has one positive divisor: itself. Therefore, it cannot be a composite number, which requires more than two positive divisors.
3. Since 1 is neither prime (as it is not greater than 1) nor composite (as it does not have more than two divisors), it fits into a separate category of numbers.

Hence, the correct conclusion is that the number 1 is neither prime nor composite.