Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.13Prime Factorization

Start hereWords, worked example, and sentence starters

Name Date Period

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.

WordWhat it meansExample
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.

I want the prime factorization of 60. I start by splitting it: 60 = 6 × 10.

  1. 6 is not prime, so I break it: 6 = 2 × 3. Both 2 and 3 are prime, so I stop those branches.
  2. 10 is not prime, so I break it: 10 = 2 × 5. Both 2 and 5 are prime, so I stop.
  3. Now every factor is prime: 60 = 2 × 2 × 3 × 5.
  4. Using exponents, I write it as 2² × 3 × 5. I check: 2 × 2 × 3 × 5 = 60. Correct.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Let's factor 12 together. What is one way to split 12 into two factors? (You might say 3 × 4.)

Answer:

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.

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.13Prime Factorization

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write a number as a product of its prime factors using a factor tree.

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort each expression: is it a COMPLETE prime factorization, or does it still have composite factors?

    Groups: Complete Prime Factorization NOT Complete (Has Composite Factors)
    • 2 × 2 × 3 (for 12)
    • 2 × 3 × 5 (for 30)
    • 2 × 2 × 2 × 3 (for 24)
    • 4 × 3 (for 12)
    • 6 × 5 (for 30)
    • 8 × 3 (for 24)

    Hint 'Complete' means every single factor shown is prime. Even one composite factor makes the whole expression NOT complete.

Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Which of the following is a prime number?

    1. A9
    2. B15
    3. C17
    4. D21

    Hint Re-read what 'prime' means: exactly two factors, 1 and itself. Any extra factor makes a number composite.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    What is the prime factorization of 30?

    1. A2 × 3 × 5
    2. B2 × 15
    3. C3 × 10
    4. D5 × 6

    Hint A prime factorization uses ONLY prime numbers. Look at each choice: are ALL of its factors prime?

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    What is the prime factorization of 18?

    1. A2 × 3 × 3
    2. B2 × 9
    3. C3 × 6
    4. D6 × 3

    Hint Check every factor in each choice — numbers like 9 and 6 are composite, so they can't appear in a prime factorization.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Which of these numbers is composite?

    1. A23
    2. B27
    3. C29
    4. D31

    Hint Composite means MORE than two factors. Ask for each number: can I split it into two smaller whole numbers?

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Find the prime factorization of 20Start: 20
    2. 2First split20 = 4 × 5
    3. 3Check each factor5 is prime, so that branch is done.
    4. 4Final answer20 = 4 × 5

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Look at every factor in the final answer — is each one a prime number?

    Correct work
    Correct answer:

Explain your thinkingHow did you decide whether a number is prime or composite? What strategy did you use?

Sentence starter I know ___ is prime because its only factors are ___ and ___. I know ___ is composite because it has factors like ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.13Prime Factorization

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write a number as a product of its prime factors using a factor tree.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each number to its prime factorization.

    1. 12
    2. 18
    3. 20
    4. 28
    5. 45
    6. 50
    • A2 × 2 × 3
    • B2 × 3 × 3
    • C2 × 2 × 5
    • D2 × 2 × 7
    • E3 × 3 × 5
    • F2 × 5 × 5
  2. 2Complete the table. Show how you found each value.

    Build the factor tree. Write each number as a product of primes.

    NumberFirst SplitPrime Factorization
    24
    36
    40
    56
    Show your work
  3. 3Write the name of the correct group on each line.

    Sort each number: can it be expressed as a product of exactly TWO prime factors, or does it need THREE or more?

    Groups: Product of Exactly Two Primes Product of Three or More Primes
    • 6
    • 10
    • 15
    • 35
    • 12
    • 30
    • 24
    • 60
  4. 4Circle the letter of the best answer. Show how you know.

    Two students found different factor trees for 60. Student A started with 2 × 30. Student B started with 6 × 10. Which statement is true?

    1. AOnly Student A gets the correct prime factorization
    2. BOnly Student B gets the correct prime factorization
    3. CThey will get different prime factorizations
    4. DBoth get the same prime factorization: 2 × 2 × 3 × 5
    Show your work
Part 2Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Find the prime factorization of 45, using exponentsStart: 45
    2. 2First split45 = 5 × 9
    3. 3Break down 99 = 3 × 3, so 45 = 5 × 3 × 3
    4. 4Write with exponents45 = 3² × 5²

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingHow did you decide whether a number is prime or composite? What strategy did you use?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.13Prime Factorization

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write a number as a product of its prime factors using a factor tree.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Write the prime factorization using exponents.

    NumberPrime Factorization (expanded)Using Exponents
    72
    100
    54
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find Marcus's Mistake

    1. 1Find prime factorization of 48Start: 48
    2. 2First split48 = 6 × 8
    3. 3Break down 66 = 2 × 3
    4. 4Break down 88 = 2 × 4
    5. 5Final answer48 = 2 × 3 × 2 × 4

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    Choose 24, 36, or 60. Show two factor trees with different first factor pairs. Finish both trees with prime factors, then explain how you checked that both products equal your chosen number.

    Write your answer

Explain your thinkingHow did you decide whether a number is prime or composite? What strategy did you use?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help