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

Lesson 6.13Prime Factorization

Set B · Version ASecond form · supported 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.

Why This Matters The space station received 60 supply crates. Mission Control needs to break this quantity into its prime components so the sorting robots can distribute them into equally sized pods. Help the crew find the prime factorization of 60!

RememberPrime Factorization

Prime Factorization & Factor Trees Prime factorization means writing a number as a product of prime numbers only. A prime number can be divided only by 1 and itself, like 2, 3, 5, and 7.

  1. Prime Number: Has exactly two factors (1 and itself, e.g. 2, 3, 5, 7, 11).
  2. Split composite number into factor pairs until every branch ends in a prime.
  3. Write final product using exponents in ascending order (e.g. 60 = 2² × 3 × 5)

Words: Prime Factorization (Factorización prima)Prime number (Número primo)Composite number (Número compuesto)Factor (Factor)Factor tree (Árbol de factores)

  1. 1Circle the letter of the best answer. Show how you know.

    What is the LCM of 6 and 9?

    1. A3
    2. B18
    3. C27
    4. D54
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    List the first four multiples of 7.

    1. A1, 7, 14, 21
    2. B7, 14, 21, 28
    3. C7, 7, 7, 7
    4. D7, 17, 27, 37
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    What is the LCM of 5 and 10?

    1. A5
    2. B10
    3. C15
    4. D50
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Hot dogs come in packs of 10 and buns in packs of 8. What is the smallest number of each you can buy with none left over?

    1. A18
    2. B20
    3. C40
    4. D80
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A station gardener is loading 72 seed pods into the greenhouse and wants to build a perfectly rectangular planting grid. Starting from the prime factorization of 72, she combines the prime factors to list every factor of 72 and choose a grid that uses all the pods. What is the prime factorization of 72?

    1. A2³ × 3²
    2. B2² × 3³
    3. C6 × 12
    4. D8 × 9
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A station gardener is loading 72 seed pods into the greenhouse and wants to build a perfectly rectangular planting grid. Starting from the prime factorization of 72, she combines the prime factors to list every factor of 72 and choose a grid that uses all the pods. The gardener wants a grid with 8 rows. How many pods in each row so all 72 are used?

    1. A6
    2. B9
    3. C12
    4. D64
    Show your work

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 ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
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

Set B · Version BSecond form · core 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.

Why This Matters The space station received 60 supply crates. Mission Control needs to break this quantity into its prime components so the sorting robots can distribute them into equally sized pods. Help the crew find the prime factorization of 60!

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

    Sort the station ID numbers: drag each one into PRIME (only 1 and itself) or COMPOSITE (more than two factors) to clear the scanner.

    Groups: Prime Numbers Composite Numbers
    • 19
    • 37
    • 41
    • 63
    • 44
    • 99
  2. 2Write the letter of the matching item on each line.

    Match each access number to its prime factorization to power up the airlock.

    1. 42
    2. 70
    3. 75
    4. 66
    5. 88
    6. 63
    • A2 × 3 × 7
    • B2 × 5 × 7
    • C3 × 5 × 5
    • D2 × 3 × 11
    • E2 × 2 × 2 × 11
    • F3 × 3 × 7
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A station gardener is loading 72 seed pods into the greenhouse and wants to build a perfectly rectangular planting grid. Starting from the prime factorization of 72, she combines the prime factors to list every factor of 72 and choose a grid that uses all the pods. Which grid would NOT use exactly all 72 seed pods?

    1. A3 by 24
    2. B4 by 18
    3. C5 by 14
    4. D6 by 12
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.
    Factor Tree for 90
    909331025

    The first lock panel shows 90. What is the prime factorization of 90?

    1. A2 × 3 × 3 × 5
    2. B2 × 45
    3. C3 × 30
    4. D9 × 10
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    The second panel needs a number whose prime factorization is 2² × 3². Which number unlocks it?

    1. A12
    2. B18
    3. C24
    4. D36
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.
    Factor Tree for 78
    7862313

    The final lock asks for the prime factorization of 78 written as a product of primes. Which is correct?

    1. A2 × 3 × 13
    2. B2 × 39
    3. C3 × 26
    4. D6 × 13
    Show your work

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

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help