Lesson Description
This lesson introduces factor trees as a visual tool to break numbers into their prime factors. You will learn how to express numbers in prime factorization form.
Learning Objectives
- Understand what prime factorization means.
- Use factor trees to break down numbers.
- Write numbers as a product of prime factors.
Key Terms
- Prime Number: A number greater than 1 with exactly two factors (1 and itself).
- Composite Number: A number with more than two factors.
- Prime Factorization: Writing a number as a product of prime numbers.
- Factor Tree: A diagram used to break a number into factors.
Example 1: Factor Tree of 24
- Start with 24.
- Break into 4 × 6.
- Break 4 into 2 × 2.
- Break 6 into 2 × 3.
- Prime factorization: 2 × 2 × 2 × 3 or 2³ × 3.
Example 2: Factor Tree of 36
- Start with 36.
- Break into 6 × 6.
- Break each 6 into 2 × 3.
- Prime factorization: 2 × 2 × 3 × 3 or 2² × 3².
Practice Problems
- Find the prime factorization of 30.
- Find the prime factorization of 45.
- Find the prime factorization of 72.
- Use exponents to write the prime factorization of 100.
Tips & Common Mistakes
- Always continue factoring until all numbers are prime.
- Different factor trees may look different but result in the same prime factorization.
- Use exponents to simplify repeated prime factors.
Summary
Factor trees help break numbers into their prime components. Prime factorization is essential for understanding GCF, LCM, and simplifying expressions.
Challenge Problems
- Find the prime factorization of 84.
- Find the prime factorization of 150.
- Explain why prime factorization is unique for every number.