Factor Foundations Guided Notes
Math Guided Notes • Number Sense
Factor Foundations
Part 1: Factors, Prime Numbers, and Composite Numbers
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Guided Definition: What is a Factor?
A factor is a whole number that divides evenly into another number with zero remainder. Factors come in pairs! For example, factor pairs of 12 are: \( 1 \times 12 \), \( 2 \times 6 \), and \( 3 \times 4 \).
1 Two Types of Whole Numbers
Prime Number Exactly 2 Factors
A number greater than 1 that has only two factors: 1 and itself.
Example: 7 is Prime
Only pair: \( 1 \times 7 = 7 \)
Factors of 7: 1, 7 (Total: exactly 2 factors)
First primes: 2, 3, 5, 7, 11, 13, 17, 19
Composite Number 3+ Factors
A number greater than 1 that has more than two factors. It can be split into smaller equal groups.
Example: 8 is Composite
Pairs: \( 1 \times 8 = 8 \) and \( 2 \times 4 = 8 \)
Factors of 8: 1, 2, 4, 8 (Total: 4 factors)
First composites: 4, 6, 8, 9, 10, 12, 14, 15
2 Step-by-Step: How to Test Any Number
Step 1: Start at 1
Every number has \( 1 \times \) itself. Write this pair down first.
Step 2: Test 2, 3, 4...
Divide by 2, 3, 4, etc. Stop when factor pairs start repeating.
Step 3: Count Total
2 factors → Prime
3+ factors → Composite
3 Guided Practice: Factor Finder & Classifier Fill in factors and check Prime or Composite
| Number | Multiplication Factor Pairs | List of All Factors | Classification |
|---|
| 9 | 1 × 9, 3 × 3 | 1, 3, 9 | Composite |
| 11 | 1 × 11 | | |
| Prime Comp | | | |
|
| 16 | 1 × 16, 2 × 8, 4 × 4 | |
Prime Comp
|
| 13 | | |
Prime Comp
|
Special Rule: The Number 1
The number 1 has only ONE factor (itself). It is neither prime nor composite!
Super Sleuth Fact: The Number 2
The number 2 is the only even prime number! All other even numbers can be divided by 2, making them composite.
Math Guided Notes • Number Sense
Greatest Common Factor (GCF)
Part 2: Definition, Guided Examples, and Scaffolded Practice
Guided Notes • Page 2
1 Guided Definition: What is GCF?
Core Concept
The Greatest Common Factor (GCF) is the largest whole number that divides evenly into two or more numbers with zero remainder.
• G = Greatest The biggest number
• C = Common Shared by both
• F = Factor Divides in evenly
2 Guided Example 1 (Modelled): Find GCF of 18 and 24
1
List all factors in order from least to greatest:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Step 2: Shared Factors 1, 2, 3, 6
Step 3: Greatest Highest match
GCF = 6
3 Guided Example 2 ("We Do"): Find GCF of 12 and 30 Complete the missing values together
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common Factors: 1, 2, 3, 6
GCF(12, 30) = 6
4 Your Turn: Scaffolded Practice Find the GCF step-by-step
Practice A: GCF of 15 and 25
Factors 15: 1, 3, _____
Factors 25: 1, 5, _____
Common:
GCF(15, 25) =
Practice B: GCF of 16 and 24
Factors 16: 1, 2, 4, _____
Factors 24: 1, 2, 3, _____
Common:
GCF(16, 24) =
Helpful Mental Math Shortcut
Does the smaller number divide evenly into the bigger number? If yes, the smaller number is the GCF (e.g. For 6 and 18, GCF is 6).
Prime pairs? GCF = 1
