Greatest Common Factor
I can find the greatest common factor (GCF) of two numbers by listing or comparing their factors.
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🎯 Content Objective / Objetivo de contenido
I can find the greatest common factor (GCF) of two numbers by listing or comparing their factors.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Mission Control must split 24 food packs and 36 water containers into equal crew pods, with each pod getting the same of each. Why won't the answer just be 24 or 36?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Space Station Supply Sort
Mission Control needs to organize 24 food packs and 36 water containers into equal groups for the crew pods. Each pod must get the same number of food packs AND the same number of water containers. What is the largest number of pods they can fill equally?
Concept Launch
💡 What is the greatest common factor (GCF)?
A factor is a number that divides another number evenly, with nothing left over. The greatest common factor is the biggest factor that two numbers share.
The GCF is the largest number that divides BOTH numbers with no remainder.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Factor Factor |
A number that divides another number with nothing left over. Un número que divide a otro sin que sobre nada. |
Factors of 12: 1, 2, 3, 4, 6, 12 — each divides 12 with no remainder | |
| Greatest Common Factor Máximo común divisor |
The biggest number that divides two or more numbers evenly. El número más grande que divide a dos o más números sin que sobre nada. |
Factors of 12: {1, 2, 3, 4, 6, 12}. Factors of 18: {1, 2, 3, 6, 9, 18}. Shared: 1, 2, 3, 6. GCF = 6 | |
| Common factor Factor común |
A number that divides two or more numbers evenly. Un número que divide a dos o más números sin que sobre nada. |
8 and 12 both divide evenly by 1, 2, and 4 — those are their common factors | |
| Divisible Divisible |
A number you can divide evenly, with nothing left over. Un número que se puede dividir sin que sobre nada. |
15 ÷ 3 = 5 with no remainder, so 15 is divisible by 3 | |
| Prime factorization Factorización prima |
Writing a number as prime numbers multiplied together. It helps you find the GCF. Escribir un número como números primos multiplicados. Ayuda a encontrar el MCD. |
12 = 2 × 2 × 3 and 18 = 2 × 3 × 3. Shared primes: 2 × 3 = 6 = GCF |
Vocabulary — True or False?
Which statements correctly use Greatest Common Factor?
Fix the False One
Which Word Fits?
A number that divides evenly into another number with no remainder is a ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
Mission Control must split 24 food packs and 36 water containers into equal crew pods, with each pod getting the same of each. Why won't the answer just be 24 or 36?
👂 Listen For
Students see the number of pods has to be a common factor of 24 and 36, so it must divide both with nothing left over, ruling out numbers that only divide one of them.
Extend: If Mission Control added one more food pack (25 packs and 36 containers), how would that change the greatest number of equal pods? Justify your reasoning.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Sort these numbers — which are factors of BOTH 24 and 36 (common factors), and which are factors of only one?
✍️ Explore Discourse
What is the greatest common factor of 24 and 36? How did sorting the factors help you find it?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
How did you find the factors that 24 and 36 share, and how did you decide which one is the GCF?
👂 Listen For
Students list common factors 1, 2, 3, 4, 6, 12 of 24 and 36 and identify 12 as the GCF because it is the largest factor shared by both.
Extend: Could you find the GCF of 24 and 36 with prime factorization instead of listing factors? Show how the shared primes give 12.
Practice Check A
A teacher has 36 pencils and 48 erasers. She wants to make identical supply bags with no items left over. What is the greatest number of bags she can make?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
What is the GCF of 8 and 12?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Ratio Table Builder
Fill the ratio table. Each row must be equivalent.
| Factor | A | B |
|---|---|---|
| ×1 | ||
| ×2 | ||
| ×3 |
✍️ Justify Your Thinking
Sort: which pairs have a GCF greater than 1, and which are relatively prime (GCF = 1)?
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "The GCF is the largest number that divides BOTH numbers with no remainder." — and it works because ___.
Because Factor means ___, but a tricky part is ___, so I have to ___.
A common mistake with Factor is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Greatest Common Factor to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
The GCF is the largest number that divides BOTH numbers with no remainder. because ___
The GCF is the largest number that divides BOTH numbers with no remainder. but ___
The GCF is the largest number that divides BOTH numbers with no remainder. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Sort these numbers — which are factors of BOTH 24 and 36 (common factors), and which are factors of only one?
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is the GCF of 8 and 12?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A baker is making gift boxes with cookies and brownies. She has 48 cookies and 32 brownies. She wants every box to have the same number of cookies and the same number of brownies, with none left over.
✍️ Connection Reasoning
How does the GCF help the baker? How many boxes can she make?
The baker can make ___ boxes because the GCF of 48 and 32 is ___.
Turn & Talk — Connect
A florist has 18 roses and 24 tulips and wants identical bouquets with no flowers left over. How does the GCF tell her the most bouquets she can make?
👂 Listen For
Students compute GCF(18, 24) = 6, so 6 bouquets, each with 3 roses and 4 tulips, and explain why a bigger number would leave flowers over.
Extend: Why does the florist use the GREATEST common factor instead of just any common factor like 3? What changes if she picks a smaller one?
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
What is the GCF of 18 and 27?
Bonus Exit Check
Which pair of numbers has a GCF of 5?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students see the number of pods has to be a common factor of 24 and 36, so it must divide both with nothing left over, ruling out numbers that only divide one of them.
• Students list common factors 1, 2, 3, 4, 6, 12 of 24 and 36 and identify 12 as the GCF because it is the largest factor shared by both.
• Students compute GCF(18, 24) = 6, so 6 bouquets, each with 3 roses and 4 tulips, and explain why a bigger number would leave flowers over.
• Students contrast GCF (largest factor that divides both, used to split into equal groups) with LCM (smallest shared multiple) and connect GCF to making equal groups with nothing left over.
Common mistake: A common mistake in Greatest Common Factor is skipping the key idea: "The GCF is the largest number that divides BOTH numbers with no remainder." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 12 bags — GCF(36, 48) = 12. She can make 12 bags, each with 3 pencils and 4 erasers.
✓ Practice 2: 4 — Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. The largest common factor is 4.
✓ Practice 3: 15 and 25 — 15 = 3 × 5, 25 = 5 × 5. Both share the factor 5, and 5 is the largest shared factor.
✓ Practice 4: 7 — Factors of 14: 1, 2, 7, 14. Factors of 21: 1, 3, 7, 21. The largest common factor is 7.
✓ Exit ticket: 9 — Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. Common: 1, 3, 9. GCF = 9.