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Prime numbers are positive integers greater than 1 that have no divisors other than 1 and themselves. On the other hand, composite numbers are positive integers greater than 1 that have divisors other than 1 and themselves. Let's explore the prime numbers less than 20 and understand the concept of prime and composite numbers in detail.
Prime Numbers Less Than 20
The prime numbers less than 20 are as follows:
2, 3, 5, 7, 11, 13, 17, 19
These are the numbers that are only divisible by 1 and themselves. For example, the number 2 is divisible only by 1 and 2, so it is a prime number. Similarly, the number 5 is divisible only by 1 and 5, so it is also a prime number.
Understanding Prime and Composite Numbers
Prime and composite numbers are fundamental concepts in number theory. Let's dive deeper into their definitions and properties:
1. Prime Numbers:
- Definition: A prime number is a positive integer greater than 1 that has no divisors other than 1 and itself.
- Examples: 2, 3, 5, 7, 11, 13, 17, 19 are prime numbers.
- Properties:
- Every prime number can be expressed as the product of itself and 1.
- Prime numbers have exactly two distinct positive divisors: 1 and the number itself.
- There are infinitely many prime numbers.
2. Composite Numbers:
- Definition: A composite number is a positive integer greater than 1 that has divisors other than 1 and itself.
- Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20 are composite numbers.
- Properties:
- Composite numbers can be expressed as the product of two or more prime numbers.
- Composite numbers have more than two distinct positive divisors.
Conclusion
Understanding prime and composite numbers is essential in mathematics. Prime numbers are positive integers greater than 1 that have no divisors other than 1 and themselves. On the other hand, composite numbers are positive integers greater than 1 that have divisors other than 1 and themselves. The prime numbers less than 20 are: 2, 3, 5, 7, 11, 13, 17, 19. These numbers play a significant role in various mathematical concepts and calculations.