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

Lesson 6.7Find Factors and Multiples

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
FactorSpanish: Factor A whole number that divides another number evenly, with no remainder. 1, 2, 4, 8, 16 divide 16.
MultipleSpanish: Múltiplo The result of multiplying a number by 1, 2, 3, and so on — where you land when you skip-count by it. Multiples of 8: 8, 16, 24, 32, 40 …
Greatest common factor (GCF)Spanish: Máximo común divisor (MCD) The largest number that is a factor of two or more numbers. It answers “how many equal groups can I make?” 48 and 36 share 1, 2, 3, 4, 6, 12 → GCF = 12
Least common multiple (LCM)Spanish: Mínimo común múltiplo (mcm) The smallest number that is a multiple of two or more numbers. It answers “when will these line up again?” 6, 12, 18, 24 and 8, 16, 24 → LCM = 24
Factor pairSpanish: Par de factores Two factors that multiply to make a number. In a word problem, one is the number of groups and the other is the size of each group. 2 × 12 = 24
Prime factorizationSpanish: Descomposición en factores primos Writing a number as a product of prime numbers, usually with a factor tree. Multiplying the primes two numbers share also gives the GCF. 24 = 2 × 2 × 2 × 3

How it worksWorked examplefinding the greatest common factor

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Find the greatest common factor of 16 and 24.

  1. List the factors of 16. 1, 2, 4, 8, 16
  2. List the factors of 24. 1, 2, 3, 4, 6, 8, 12, 24
  3. Mark the factors that are in both lists. 1, 2, 4, 8
  4. Pick the greatest shared factor. GCF = 8

Answer: The greatest common factor of 16 and 24 is 8.

Now you trySame steps, your turn

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

Find the greatest common factor of 20 and 35.

  1. List the factors of 20.
  2. List the factors of 35.
  3. Mark the factors that are in both lists.
  4. Pick the greatest shared factor. GCF =
Answer:greatest common factor of 20 and 35

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The factors of are .
  • The factors that both numbers share are .
  • The greatest common factor is .
  • I used the GCF here because the problem asks for .

Word bank factorfactor paircommon factorgreatest common factorGCFprimeprime factorizationdivides evenlylistsharegreatestequal groups

Watch outA common mistake

A common mistake is reaching for the wrong tool: listing FACTORS for a problem about repeating cycles. Ayasha's classes repeat every 6 and 8 weeks, so the weeks they land on are multiples — answering with the GCF of 2 claims a class that meets every 8 weeks happens in week 2. Use the size of the answer as a check: a GCF is never larger than the smaller number, and an LCM is never smaller than the larger one.

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

Lesson 6.7Find Factors and Multiples

Version ASupported practice

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

Learning target I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.

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

    Sort each number by its relationship to 10.

    Groups: A factor of 10 only A multiple of 10 only Both a factor and a multiple of 10
    • 2
    • 20
    • 5
    • 30
    • 10
    • 50

    Hint Check both relationships: does this number divide 10 evenly, and does 10 divide this number evenly?

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

    Which list shows all the factors of 12?

    1. A1, 2, 3, 4, 6, 12
    2. B1, 12
    3. C2, 3, 4, 6
    4. D12, 24, 36, 48

    Hint Ask: what divides 12 with nothing left over?

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

    Which list shows the first four multiples of 8?

    1. A1, 2, 4, 8
    2. B2, 4, 6, 8
    3. C8, 16, 24, 32
    4. D8, 9, 10, 11

    Hint Skip-count by 8 out loud.

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

    What is the greatest common factor of 12 and 18?

    1. A2
    2. B3
    3. C6
    4. D36

    Hint List the factors of each number.

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

    What is the least common multiple of 4 and 6?

    1. A2
    2. B10
    3. C12
    4. D24

    Hint List multiples of each number.

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

    Find the error

    1. 1ProblemFind the GCF of 12 and 18.
    2. 2Step 1Factors of 12: 1, 2, 3, 4, 6, 12
    3. 3Step 2Factors of 18: 1, 2, 3, 6, 9, 18
    4. 4Step 3The GCF is 36, because 36 is in both times tables.

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

    Hint Compare Step 3's answer to the two numbers themselves.

    Correct work
    Correct answer:

Explain your thinkingBoth problems say “common.” How do you decide whether a problem wants the GCF or the LCM?

Sentence starter If the problem ___ something into equal groups, I use the ___. If it asks when things ___ again, I use the ___.

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 6.7Find Factors and Multiples

Version BCore practice

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

Learning target I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.

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

    The store has 48 pencils and 36 notebooks. Complete the factor lists, then find the GCF.

    NumberFactorsGCF
    481, 2, 3, 4, 6, 8, 12, 16, 24, 48
    36
    Show your work
  2. 2Write the name of the correct group on each line.

    Sort each real problem by the tool that solves it.

    Groups: Use the GCF Use the LCM
    • Split 48 pencils and 36 notebooks into identical packs
    • Two classes repeat every 6 and 8 weeks — when do they meet?
    • Cut two ribbons into the longest equal pieces with none left over
    • Hot dogs in packs of 10, buns in packs of 8 — when do they match?
    • The answer is at most the smaller number
    • The answer is at least the larger number
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Using prime factors, 48 = 2 × 2 × 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3. What is their GCF?

    1. A2, the only prime they share
    2. B6, from one 2 and one 3
    3. C12, from the shared 2 × 2 × 3
    4. D144, from multiplying all the primes
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Ayasha has painting every 8 weeks and pottery every 6 weeks, both this week. When do they next fall in the same week?

    1. AIn 2 weeks
    2. BIn 14 weeks
    3. CIn 24 weeks
    4. DIn 48 weeks
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1ProblemAyasha has painting every 8 weeks and pottery every 6 weeks. When do both fall in the same week?
    2. 2Step 1Factors of 8: 1, 2, 4, 8
    3. 3Step 2Factors of 6: 1, 2, 3, 6
    4. 4Step 3The greatest common factor is 2, so both classes meet in week 2.

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

    Correct work
    Correct answer:

Explain your thinkingBoth problems say “common.” How do you decide whether a problem wants the GCF or the LCM?

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 6.7Find Factors and Multiples

ChallengeExtension

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

Learning target I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.

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

    Find both the GCF and the LCM of each pair.

    NumbersGCFLCM
    6 and 8224
    12 and 18
    4 and 10
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1ProblemFind the LCM of 6 and 8.
    2. 2Step 1Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
    3. 3Step 2Multiples of 8: 8, 16, 24, 32, 40, 48
    4. 4Step 3Both lists contain 48, so the LCM is 48.

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

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

    Reginald is having hot dogs for 24 guests and wants the same number of hot dogs and buns, with none left over. Hot dogs come in packs of 10 and buns in packs of 8. How many packs of each should he buy, and how many will he have? Explain which tool you used and why.

    Write your answer

Explain your thinkingBoth problems say “common.” How do you decide whether a problem wants the GCF or the LCM?

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