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Good Morning!. Please have the following on your desk Math Binder INB Pencil White board Whiteboard marker. 3-2 Greatest Common Divisor (GCD ) OR Greatest Common Factor (GCF). Objective: I can find the greatest common divisor of two or more whole numbers.

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Presentation Transcript
Good morning
Good Morning!

  • Please have the following on your desk

    • Math Binder

    • INB

    • Pencil

    • White board

    • Whiteboard marker


3 2 greatest common divisor gcd or greatest common factor gcf
3-2 Greatest Common Divisor (GCD)OR Greatest Common Factor (GCF)

Objective: I can find the greatest common divisor of two or more whole numbers.

Now set up the left side of the page & complete:

  • Page number:

  • Lesson title: Greatest Common Divisor/Factor

  • Learning goal: (write the objective in your own words)

  • What I know: (Write 1 or 2 sentences explaining what you already know about the lesson)


California

Standards

Preparation for NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form for a fraction).


Why learn this?

Party Planners can use the greatest common divisor to find the number of matching centerpieces they can make.


Vocabulary
Vocabulary

greatest common divisor (GCD)

OR

greatest common factor (GCF)


The greatest common divisor (GCD) of two or more whole numbers is the greatest whole number that divides evenly into each number.

One way to find the GCD of two or more numbers is to list all the factors of each number. The GCD is the greatest factor that appears in all the lists.


Foldable closed

Foldable open


Additional Example 1:Using a List to Find the GCD

Find the greatest common divisor (GCD) of 12, 36, and 54.

USE THE SLIDE/LADDER/UPSIDE DOWN DIVISION METHOD!!!


Find the greatest common divisor of 14, 28, and 63.

SLIDE METHOD!

Check It Out! Example 1


Additional Example 2A: Using Prime Factorization to Find the GCD

Find the greatest common divisor (GCD).

40, 56

Slide Method!


Additional example 2b using prime factorization to find the gcd
Additional Example 2B: Using Prime Factorization to Find the GCD

Find the greatest common divisor (GCD).

252, 180, 96, 60

Slide Method!


Check it out example 2a
Check It Out! Example 2A to Find the GCD

Find the greatest common divisor (GCD).

72, 84

Slide Method!


Your turn
YOUR TURN to Find the GCD

Find the greatest common divisor (GCD).

1. 28, 40 2. 24, 56

3. 54, 99 4. 20, 35, 70

5. The math clubs from 3 schools agreed to a competition. Members from each club must be divided into teams, and teams from all clubs must be equally sized. What is the greatest number of members that can be on a team if Georgia has 16 members, Williams has 24 members, and Fulton has 72 members?


Common core activity
Common Core Activity to Find the GCD

  • 1. Stand up

  • 2. Hold your hand up

  • 3. The first person you see, slap hands and say what the G stands for in GCD

  • 4. The next person you see slap hands say what the C stands for in GCD

  • 5. The next person you see slap hands, say what the D stands for in GCD

  • 6. The last person say what GCD stands for!


Left side time
Left side time! to Find the GCD

  • What I learned: write 1-2 sentences about what you learned.

    Proof: Using the slide method, find the GCD of 28, 40

  • Reflection:What’sthe error? A student used these factor trees to find the GCD of 50 and 70. The student decided that the GCD is 5. Explain the student’s error and show how to get the correct GCD.


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