Multi-Digit and Fraction Computation

Lesson 15

Objective

Find the greatest common factor of two numbers. Solve application problems using the greatest common factor. 

Common Core Standards

Core Standards

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  • 6.NS.B.4 — Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Foundational Standards

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  • 4.OA.B.4

Criteria for Success

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  1. Define and understand the greatest common factor (GCF) as the greatest whole number that is a factor of each number. 
  2. Find the greatest common factor by listing and comparing the factor pairs of each number.
  3. Find the greatest common factor by finding the prime factorization of each number and identifying the common prime factors. 
  4. Define and understand relatively prime numbers as two whole numbers whose only common factor is 1.
  5. Solve word problems that involve finding the greatest common factor.

Tips for Teachers

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Understanding the greatest common factor of two numbers will support students in their work in Unit 5, Numerical and Algebraic Expression, where they will use common factors and the distributive property to write expressions in factored form.

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Anchor Problems

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Problem 1

Find the greatest common factor of 12 and 18.

  • List all of the factor pairs of 12 and of 18.
  • Circle the factors that appear in both lists.
  • Place a triangle around the greatest of these common factors.

Use this same method to find the greatest common factor of 48 and 56.

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic D > Lesson 18Example 1

Grade 6 Mathematics > Module 2 > Topic D > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Find the greatest common factor of 12 and 18 using prime factorization.

  • Write 12 and 18 as products of prime factors using prime factorization.
  • Draw a Venn diagram with prime factors of 12 in one circle and of 18 in another circle. 
  • Use the Venn diagram to find the greatest common factor.

Use this same method to find the greatest common factor of 48 and 56.

Use this same method to find the greatest common factor of 8 and 25. What happens in this example? 

Guiding Questions

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Problem 3

Jasmine’s family is having a family picnic. Jasmine is planning on ordering enough pizza to have 96 slices and a tray of 72 cookies. She wants to make sure each family member gets the same number of cookies and slices of pizza. Based on this food order, what is the greatest number of family members Jasmine can invite to the picnic? How many slices of pizza and cookies will each family member get?  

Guiding Questions

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Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include problems where students must determine two numbers that have a given greatest common factor; for example: Name 2 numbers that have 12 as a greatest common factor.
  • Include examples of relatively prime numbers.

Target Task

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  1. List all the factors of 48.
  2. List all the factors of 64.
  3. What are the common factors of 48 and 64?
  4. What is the greatest common factor of 48 and 64?

References

Illustrative Mathematics Factors and Common Factors

Factors and Common Factors, accessed on Sept. 28, 2017, 4:31 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Mastery Response

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