Lesson Description
This lesson focuses on identifying all factors of numbers, understanding factor properties, and using factors to solve problems.
Learning Objectives
- Define what a factor is.
- List all factors of a given number.
- Apply factors to solve problems and simplify calculations.
Topics Covered
- Definition of factors
- Listing factors of numbers
- Properties of factors
- Using factors in problem-solving
Key Terms
- Factor: A number that divides another number evenly without leaving a remainder.
- Divisor: Another term for factor.
- Composite Number: A number with more than two factors.
Lesson Examples
Example 1: Finding Factors of 20
- Start with 1 and 20: 1×20=20 → 1 and 20 are factors.
- Check 2: 2×10=20 → 2 and 10 are factors.
- Check 3: 20 ÷ 3 = 6.666… → not a factor.
- Check 4: 4×5=20 → 4 and 5 are factors.
- All factors of 20: 1, 2, 4, 5, 10, 20.
Example 2: Factors of 18
- 1×18=18 → 1, 18
- 2×9=18 → 2, 9
- 3×6=18 → 3, 6
- All factors: 1, 2, 3, 6, 9, 18
Practice Problems
- List all factors of 24.
- List all factors of 36.
- Is 7 a factor of 56?
- Identify whether 12 is a factor of 144.
Tips & Common Mistakes
- Always start with 1 and the number itself when listing factors.
- Check divisibility by integers sequentially to avoid missing factors.
- Do not include numbers that do not divide evenly.
Summary
Factors are numbers that divide evenly into a given number. Identifying all factors is crucial for understanding prime factorization, LCM, GCF, and solving arithmetic problems efficiently.
Challenge Problems
- List all factors of 60 and 90. Identify the common factors.
- Find all factors of a 2-digit prime number and explain the result.
- Create a word problem involving factors and solve it.