Lesson 6.136.13 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can write a number as a product of its prime factors using a factor tree — one step at a time, with support.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Prime FactorizationSpanish: Factorización prima | Writing a whole number as a product of only prime numbers. | 36 = 2 × 2 × 3 × 3 = 2² × 3² |
| Prime numberSpanish: Número primo | A number bigger than 1 that you can only divide by 1 and itself. | 7 has only two factors: 1 × 7. So 7 is prime. |
| Composite numberSpanish: Número compuesto | A number bigger than 1 that you can divide by more than just 1 and itself. | 12 = 1 × 12, 2 × 6, 3 × 4 — six factors, so 12 is composite |
| FactorSpanish: Factor | A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4. | Factors of 12: 1, 2, 3, 4, 6, 12 — each divides 12 evenly. |
| Factor treeSpanish: Árbol de factores | A picture that splits a number into its prime numbers, step by step. | 24 → 4 × 6 → (2 × 2) × (2 × 3) → 2 × 2 × 2 × 3 |
| ExponentSpanish: Exponente | A small number that tells how many times to multiply a number by itself. | 2³ means 2 × 2 × 2 = 8 |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Find the prime factorization of 60.
- Split 60 into two factors: 60 = 6 × 10
- Split 6, because 6 is not prime: 6 = 2 × 3
- Split 10, because 10 is not prime: 10 = 2 × 5
- Write all the prime factors from least to greatest: 60 = 2 × 2 × 3 × 5
- Use an exponent for the two 2s: 2 × 2 × 3 × 5 → 2² × 3 × 5
- 60 = 2 × 2 × 3 × 5. With an exponent, it is 2² × 3 × 5.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Find the prime factorization of 12.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I know is prime because its only factors are and . I know is composite because it has factors like .
Word bank Prime FactorizationPrime numberComposite numberFactorFactor treeExponentprimecompositefactorsdivisibletwo factorsmore than two
Watch outA common mistake
A common mistake in Prime Factorization is stopping the factor tree too soon — leaving a composite number like 4, 6, 8, or 9 in the final answer instead of continuing to split it. For example, writing 20 = 4 × 5 as the prime factorization (4 is composite) instead of finishing with 20 = 2 × 2 × 5. Before you submit, check every number in your final answer: if any factor can still be broken into smaller factors, the tree isn't finished yet.
Lesson 6.136.13 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can write a number as a product of its prime factors using a factor tree — one step at a time, with support.
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1Complete each step, then write the final answer.
Keep splitting until every end is prime. Find the prime factorization of 36. Use a factor tree.
- 1Split 36 into 4 × 9. Is 4 prime? Is 9 prime?
- 2Split 4 and 9 into primes.
- 3Fill in the blank: 36 = 2 × 2 × 3 × ___.
- 4Write it with exponents.
Final answer: -
2Complete each step, then write the final answer.
45 is odd, so 2 is not a factor. Find the prime factorization of 45. This number is odd.
- 145 is odd, so 2 does not work. Try 5 × 9. Is 5 prime?
- 2Is 9 prime? Split it if it is not.
- 3How many 3s are in the prime factorization of 45?
Final answer: -
3Complete each step, then write the final answer.
Fill in the blank: 18 = 2 × 3 × ___.
Show your workHint Start with 18 = 2 × 9. Then split 9.
Final answer: -
4Complete each step, then write the final answer.
Make a factor tree for 48. How many 2s are in its prime factorization?
Show your workHint Start with 48 = 6 × 8. Keep splitting until every branch is prime. Then count the 2s.
Final answer: -
5Complete each step, then write the final answer.
A teacher has 70 stickers. She writes 70 as a product of primes to plan equal groups: 70 = 2 × 5 × ___. What is the missing prime?
Show your workHint Start with 70 = 7 × 10. Then split 10.
Final answer: -
6Complete each step, then write the final answer.
Kai says the prime factorization of 24 is 2 × 3 × 4. He is not done. Which of his factors is not prime?
Show your workHint A prime number has exactly two factors, 1 and itself. Test each factor.
Final answer:
Explain your thinkingHow do you know when a factor tree is finished? Use Kai's mistake with 24 to explain.
Sentence starter A branch stops when the number is ___. · Kai was not done because ___.