# Greatest Common Factor

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## Objective

SWBAT find GCF of 2 or more numbers.

#### Big Idea

Students find what they have in common and what numbers have in common.

## Do Now

15 minutes

Students are seated in groups of four, for this activity I will ask them to partner up with someone in their group.  Most students are familiar with a Venn diagram, but I will explain that the section where the circles overlap should be filled in with what they have in common and the portion where they don't overlap should be completed with their differences.  I will give them the following directions:

With your partner, discuss your similarities and differences. (MP1) Complete the Venn diagram together based on what you learned about each other. Getting to Know You Venn Diagram.docx

- What is your favorite color?

- Who is your favorite singer?

- Do you have any brothers/sisters?

After about 10 minutes, I will randomly select a few students to discuss their Venn Diagram.

## Activity

10 minutes

For this activity, I will give each group of students manipulatives of 24 blocks and 36 circular chips.  I will explain to students that these represent the chocolate bars and lollipops.  They will have to use these manipulatives to answer the questions for the situation below.

Party Favors!

You are planning a party and want to give your guests party favors. You have 24 chocolate bars and 36 lollipops.

Discussion Questions

- What is the greatest number of party favors you can make if each bag must have exactly the same number of chocolate bars and exactly the same number of lollipops? You do not want any candy left over. Explain.

- Could you make a different number of party favors so that the candy is shared equally? If so, describe each possibility.

- Which possibility allows you to invite the greatest number of guests? Why?

Some groups may have difficulty, but I will let them discuss the possibilities, offering advice if necessary.  If groups have answered the first question correctly, I will tell them to move on to the other questions.

After about 10 minutes, I will reconvene the class to discuss their findings.  I will conclude the activity with the question, "Is there another mathematical way of finding the answer?"  This will lead to the lesson.

## Mini-Lesson

15 minutes

I will provide students with 2 different methods of finding the Greatest Common Factor.  I will explain to students that both methods are good, but method 2 works well when they are given larger numbers.

Method 1:  List the Factors  GCF - Method 1

Students may know this method as the rainbow method.  I will stress that if they use this method, it is important to find all the factors.  The divisibility rules will help them.  This method works well when students think of the factor pairs of a number until they have listed all of the factors.

Method 2:  The Division Method and Venn Diagram Method  GCF - Method 2

Students will use the division method (previously taught in Prime Factorization lesson) to find the prime factors the numbers.  Once they find the prime factors, we will complete the venn diagram.  I will remind students that similar to what they had in common, the factors the numbers have in common should be put in the overlapping section of the diagram.  It is important to circle the common factors to ensure that they don't use them more them once.  To find the GCF, I will explain that they need to find the product of the numbers in the overlapping section.

## Independent Practice

10 minutes

I will give students a few problems to practice on their own.  As students work, I will circulate around the class to answer any questions and to assess understanding.  A common mistake that students make is when placing the common factors in the overlapping section, they write the number twice.

Find the GCF of:

1.  60 and 72

2.  240 and 620

I will encourage students to check their work and verify their answer with their group members.

## Lesson Review

5 minutes

I will ask students to share any advice for their classmates in finding the GCF.

Students may offer help, such as

1. use the divisibility rules to find factors

2.  only prime numbers are on the outside of the "cake"