Prime Numbers vs Composite Numbers

Prime Numbers

• Definition: A prime number is a number that can only be divided by 1 and itself without leaving a remainder.
  • Only factors are 1 and itself.
  • Exception: The number 1 is not considered a prime number.
• Examples:
  • 2: Factors are 1 and 2 (only even prime number).
  • 3: Factors are 1 and 3.
  • 5: Factors are 1 and 5.
  • 7, 11, 13, 17, 19, 23, 29, etc.
• Characteristics:
  • 2 is the only even prime number because all other even numbers are divisible by 2.
  • No simple method to determine if a number is prime; requires checking divisibility by numbers other than 1 and itself.

Composite Numbers

• Definition: A composite number is any number that is not prime, except for 1 which is neither prime nor composite.
  • Has factors other than 1 and itself.
• Examples:
  • 4: Divisors include 1, 2, and 4.
  • 6: Divisors include 1, 2, 3, and 6.
  • 8, 9, 10, etc.

Key Points

• Number 1: Neither prime nor composite.
• Determining Primality:
  • Check divisibility for numbers other than 1 and itself to confirm prime status.

Conclusion

• Understanding the distinction between prime and composite numbers is crucial for number theory.
• Prime numbers have limited divisors, while composite numbers have multiple divisors.