Lesson 6.136.13 · Part II
Start hereWords, worked example, and sentence starters
Learning target I can write a number as a product of its prime factors using a factor tree.
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 |
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
Word bank Prime FactorizationPrime numberComposite numberFactorFactor treeExponent
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 · Part II
Apply Day · Version ASupported practice
Learning target I can write a number as a product of its prime factors using a factor tree.
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1Complete each step, then write the final answer.
Fill in the blank: 20 = 2 × 2 × ___.
Show your workHint Start with 20 = 4 × 5. Then split 4.
Final answer: -
2Complete each step, then write the final answer.
Fill in the blank: 66 = 2 × 3 × ___.
Show your workHint Start with 66 = 6 × 11. Then split 6.
Final answer: -
3Complete each step, then write the final answer.
Fill in the blank: 27 = 3 × 3 × ___.
Show your workHint Start with 27 = 3 × 9. Then split 9.
Final answer:
Lesson 6.136.13 · Part II
Apply Day · Version BCore practice
Learning target I can write a number as a product of its prime factors using a factor tree.
-
1Complete 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 workFinal answer: -
2Complete each step, then write the final answer.
Find the prime factorization of 54. What is the exponent on 3?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Fill in the blank: 50 = 2 × 5 × ___.
Show your workFinal answer:
Lesson 6.136.13 · Part II
Apply Day · ChallengeExtension
Learning target I can write a number as a product of its prime factors using a factor tree.
-
1Circle the letter of the best answer. Show how you know.
What is the prime factorization of 72?
- A2³ × 3²
- B2² × 3³
- C2 × 3 × 12
- D8 × 9
Show your work -
2Complete each step, then write the final answer.
Ben says 3² × 5 and 3 × 5² are the same number because they use the same primes. Find 3 × 5².
Show your workFinal answer: -
3Complete each step, then write the final answer.
Find the prime factorization of 150. What is the exponent on 5?
Show your workFinal answer: