A natural number (i.e. 1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it has exactly two positive factors, 1 and the number itself. Natural numbers that have more than two positive factors are called composite. 1 has only one positive factor i.e. no.1 only. Hence 1 is neither prime nor composite.

1 is neither a prime number nor a composite number . It is a unique number .

Understanding the Number 1
The number 1 holds a unique position in the world of mathematics. It is neither a prime number nor a composite number. Here’s a detailed explanation:
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.
- Examples include 2, 3, 5, 7, etc.
Definition of Composite Numbers
- A composite number is a natural number greater than 1 that has more than two positive divisors.
- Examples include 4, 6, 8, 9, etc.
Why is 1 Not Considered Prime or Composite?
- Single Divisor: The number 1 has only one positive divisor, which is itself. This does not meet the criteria for being prime, as prime numbers must have exactly two distinct divisors.
- Exclusion from Composite: Since composite numbers require more than two divisors, 1 cannot be classified as composite either.
Mathematical Consensus
- Throughout history, mathematicians have reached a consensus that 1 is a unique entity.
- Its classification helps maintain the integrity of the definitions of prime and composite numbers.
Conclusion
- The number 1 is a unique natural number that stands alone in its category.
- It is neither prime nor composite, making it a foundational number in mathematics.
Understanding the role of 1 is crucial for further studies in number theory and mathematics as a whole.