Lesson Description
This lesson teaches you how to identify prime and composite numbers, understand their unique properties, and use them in factorization problems and divisibility rules.
Learning Objectives
- Define prime and composite numbers.
- Identify prime and composite numbers up to 100.
- Use prime numbers in factorization and divisibility problems.
Key Terms
- Prime Number: A number greater than 1 with exactly two factors: 1 and itself.
- Composite Number: A number greater than 1 with more than two factors.
- Divisibility: The ability of one number to be divided evenly by another.
Example 1: Identifying Prime Numbers
- Check 13: Factors are 1 and 13 only → Prime.
- Check 15: Factors are 1, 3, 5, 15 → Composite.
- Check 29: Factors are 1 and 29 → Prime.
Example 2: Identifying Composite Numbers
- Check 18: Factors are 1, 2, 3, 6, 9, 18 → Composite.
- Check 21: Factors are 1, 3, 7, 21 → Composite.
- Check 31: Factors are 1 and 31 → Prime.
Practice Problems
- Determine whether the numbers 17, 20, 23, 28 are prime or composite.
- List all prime numbers between 1 and 50.
- Find two composite numbers whose factors include 2 and 3.
- Check if 49 is prime or composite.
Tips & Common Mistakes
- Remember 1 is neither prime nor composite.
- Always check all possible factors before deciding if a number is prime.
- Do not assume odd numbers are always prime.
Summary
Prime numbers have exactly two factors, while composite numbers have more than two. Recognizing these numbers is essential for factorization, divisibility, and advanced problem-solving.
Challenge Problems
- Find all prime numbers between 50 and 100.
- Determine whether 91, 97, and 99 are prime or composite.
- Explain why 2 is the only even prime number.