📝 Practice Worksheets
🛠️ Related Tools
🔑 Key Concepts
- A prime number has exactly two factors: \( 1 \) and itself.
- A composite number has more than two factors.
- Every composite number can be written as a product of prime numbers.
- Prime factorization shows the prime numbers multiplied together to make a composite number.
- Important: the number \( 1 \) is neither prime nor composite.
✏️ Worked Examples – Factor Lists and Prime Factorization
🧠 Math Vocabulary
- Prime Number: a whole number greater than \( 1 \) with exactly two factors.
- Composite Number: a whole number greater than \( 1 \) with more than two factors.
- Factor: a number that divides another number evenly.
- Prime Factorization: writing a composite number as a product of prime numbers.
- Exponential Notation: a shortened way to write repeated multiplication of the same factor.
💡 Main Idea
This lesson shows that every composite number can be broken into prime numbers. Students identify prime and composite numbers, build complete factor lists, and then organize repeated prime factors using exponential notation. Seeing how factor lists connect to prime factorization strengthens number sense and prepares students for later work with GCF, LCM, and simplifying expressions.
📚 What You Should Already Know
Students should already know basic multiplication facts, division facts, and how to recognize factor pairs. It also helps if students understand that a factor divides a number evenly and that repeated multiplication can be written more efficiently with exponents.
🚀 What Comes Next
After students understand prime and composite numbers and how to write prime factorizations, they are ready to apply these ideas to greatest common factor, least common multiple, simplifying fractions, and more advanced work with exponents and number properties.
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