Unit 1 · Standard 6.NS.4
Greatest Common Factor
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Factors of 12: 1, 2, 3, 4, 6, 12 — each divides 12 with no remainder
Factor
A number that divides another number with nothing left over.
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
Greatest Common Factor
The biggest number that divides two or more numbers evenly.
8 and 12 both divide evenly by 1, 2, and 4 — those are their common factors
Common factor
A number that divides two or more numbers evenly.
15 ÷ 3 = 5 with no remainder, so 15 is divisible by 3
Divisible
A number you can divide evenly, with nothing left over.
12 = 2 × 2 × 3 and 18 = 2 × 3 × 3. Shared primes: 2 × 3 = 6 = GCF
Prime factorization
Writing a number as prime numbers multiplied together. It helps you find the GCF.
Key Ideas & Notes
- 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?
- Sort these numbers — which are factors of BOTH 24 and 36 (common factors), and which are factors of only one?
Think About It
- What two quantities need to be divided equally?
- What numbers could divide into both 24 and 36?
- What's the biggest number of equal groups we can make?
My Notes
Guided Examples
Example 1
What is the GCF of 8 and 12?
Solution: Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. The largest common factor is 4.
Answer: A. 4
Example 2
Which pair of numbers has a GCF of 5?
Solution: 15 = 3 × 5, 25 = 5 × 5. Both share the factor 5, and 5 is the largest shared factor.
Answer: A. 15 and 25
Example 3
What is the GCF of 14 and 21?
Solution: Factors of 14: 1, 2, 7, 14. Factors of 21: 1, 3, 7, 21. The largest common factor is 7.
Answer: A. 7
Write About the Math The Writing Revolution
I can explain how I found the GCF using the words factor, common factor, divisible, and greatest common factor.
1. Kernel Sentence subject + verb
Model: Factor is a number that divides another number with nothing left over.Factor es un número que divide a otro sin que sobre nada.
Write a kernel sentence about factor. Use a subject and a verb.Escribe una oración base sobre factor. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Factor matters in mathFactor importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Factor matters in math because ___.Factor importa en matemáticas porque ___.
Factor matters in math, but ___.Factor importa en matemáticas, pero ___.
Factor matters in math, so ___.Factor importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about factor.Di un hecho verdadero sobre factor.
Factor ___.
Ask a question about factor.Haz una pregunta sobre factor.
How does ___ ?¿Cómo ___ ?
Show excitement about factor.Muestra entusiasmo sobre factor.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with factor.Dile a un compañero qué hacer con factor.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The common factors are ___.Los factores comunes son ___.
The greatest common factor is ___ because ___.El máximo común divisor es ___ porque ___.
I would use the GCF to ___.Usaría el MCD para ___.
Try It
Solve on your own. Check the answer key when you are done.
1. What is the GCF of 9 and 15?
- 3
- 1
- 9
- 45
2. 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?
- 12 bags
- 6 bags
- 4 bags
- 36 bags
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A farmer has 48 apples and 32 oranges. She wants to make gift baskets where every basket has the same number of apples and the same number of oranges, with none left over. Find the greatest number of baskets and explain how you used GCF to solve this.
Sentence starter: The GCF of 48 and 32 is ___ because ___. So the farmer can make ___ baskets, each with ___ apples and ___ oranges.
Reflect — Exit Ticket
What is the GCF of 18 and 27?
- 9
- 3
- 6
- 18
Answer Key & Teacher Guide
- Try It 1: A. 3 — Factors of 9: 1, 3, 9. Factors of 15: 1, 3, 5, 15. The largest common factor is 3.
- Try It 2: A. 12 bags — GCF(36, 48) = 12. She can make 12 bags, each with 3 pencils and 4 erasers.
- Exit Ticket: A. 9 — Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. Common: 1, 3, 9. GCF = 9.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Factor is a number that divides another number with nothing left over.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).