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

Lesson 6.136.13 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

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.

Ana makes a factor tree for 72. She starts with 8 × 9. Find the prime factorization of 72. Use exponents.

  1. Split 72 into 8 × 9: 72 = 8 × 9
  2. Split 8 until every branch is prime: 8 = 2 × 4 → 4 = 2 × 2
  3. Split 9: 9 = 3 × 3
  4. Write the primes. Use exponents for repeats: 72 = 2 × 2 × 2 × 3 × 3; 2 × 2 × 2 × 3 × 3 → 2³ × 3²
  5. The prime factorization of 72 is 2³ × 3².
  6. Ben also makes a factor tree for 72. He starts with 2 × 36. Does he get the same prime factorization as Ana?
  7. Split 72 into 2 × 36: 72 = 2 × 36
  8. Split 36 into 4 × 9: 36 = 4 × 9
  9. Split 4 and 9 into primes: 4 = 2 × 2 → 9 = 3 × 3
  10. Compare Ben's primes with Ana's primes: 2 × 2 × 2 × 3 × 3 → 2³ × 3²
  11. Yes. Ben also gets 2³ × 3². Both trees give the same primes.

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. Then explain what happens if you start a different way.

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 6.136.13 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    81080
    Lia starts with 8 × 10.

    Lia makes a factor tree for 80. She starts with 8 × 10. Find the prime factorization of 80. Use exponents.

    1. 1Split 8 and 10 until every branch is prime.
    2. 2How many 2s are there in all?
    3. 3Write 80 with exponents.
    Final answer:
  2. 2Complete each step, then write the final answer.
    24080
    Omar starts with 2 × 40.

    Omar also makes a tree for 80, but he starts with 2 × 40. Does he get the same prime factorization as Lia?

    1. 1Split 40 until every branch is prime.
    2. 2How many 2s does Omar's tree end with?
    3. 3Why do Lia and Omar get the same primes?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the prime factorization of 54. What is the exponent on 3?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    A number has the prime factorization 2² × 3 × 5². What is the number?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A baker has 98 cookies. She writes 98 as a product of primes to plan equal boxes. Which prime appears two times?

    Show your work
    Final answer:
  6. 6Complete 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 work
    Final answer:

Explain your thinkingLia and Omar started their trees for 80 in different ways. Why must they end with the same primes?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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