1. Greatest Common Factor Least Common Multiple Prime Factorization
6th Grade Mathematics
Miss Quimby’s Class

2. Table of Contents Lesson 1: What are prime and composite numbers?
Lesson 2: How is the prime factorization of a number determined?
Lesson 3: How is the greatest common factor of two or more numbers found?
Lesson 4: How is the least common multiple of two or more numbers found?
Lesson 5: How is upside-down division used to find prime factorization, GCF, and LCM?
Click on the lesson that you wish to go to.

3. What do these three pictures have in common?
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PRIMary colors, Optimus PRIME, PRIME Number. Show this slide to the students and have them guess what they have in common. You may want to write their guesses on the board. There are no wrong answers. This is just to introduce the new lesson.
The are all prime!

4. Key Vocabulary Page On the top of the next clean page write:
GCF/LCM/Prime Factorization Vocabulary
Create a word column and a definition column
Paperclip the next 2 pages together.
Keep track of all new vocabulary on these pages.
At the end of the unit you will have a key vocabulary list to use to study.
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Pass out a new paper clip to each student to keep track of where the new unit begins.

5. EQ: What are prime and composite numbers?
Key Vocabulary
Prime Number: Any whole number, greater than 1, that can only be divided evenly by 1 and itself.
Example:
3 can only be divided by 3 and 1.
3 ÷ 3 = 1
3 ÷ 1 = 3
Composite Number: Any whole number, greater than 1, that can be divided evenly by a number other than 1 or itself.
4 can be divided by 4, 1, and 2
4 ÷ 4 = 1
4 ÷ 1 = 4
4 ÷ 2 = 2
With no remainder
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EQ: What are prime and composite numbers?

6. EQ: What are prime and composite numbers?
Divisibility Rules
To quickly tell if a number is prime or composite use the following rules:
A number is divisible by:
2 if the ones digit is divisible by 2
3 if the sum of the digits is divisible by 3
5 if the ones digit is 0 or 5
6 if the number is divisible by both 2 and 3
9 if the sum of the digits is divisible by 9
10 if the ones digit is 0.
Keep in mind that some numbers do NOT have rules!
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EQ: What are prime and composite numbers?

7. EQ: What are prime and composite numbers?
Examples
1. Is 46 divisible by 2?
The ones digit is 6.
Since 6 ÷ 2 = 3, 46 is divisible by 2.
2. Is 428 divisible by 3?
The sum of the digits is = 14.
Since 14 is not divisible by 3, 428 is not divisible by 3.
3. Is 2,736 divisible by 9?
The sum of the digits is = 18.
Since 18 ÷ 9 = 2, 2,736 is divisible by 9.
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EQ: What are prime and composite numbers?

8. EQ: What are prime and composite numbers?
Prime vs. Composite
Every number is either prime or composite.
Use the divisibility rules
Ask yourself, “Is there anything that can divide evenly into this number other than itself and 1?”
Yes- composite.
No- prime.
ODD does NOT equal Prime!
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EQ: What are prime and composite numbers?

9. EQ: What are prime and composite numbers?
Examples
1. Is 18 a prime or composite number?
Does anything other than 1 and 18 divide evenly into 18?
Yes, 2, 3, 6, and 9.
So, 18 is composite.
2. Is 29 a prime or composite number?
Does anything other than 1 and 29 divide evenly into 29?
No, only 1 and 29.
So, 29 is prime.
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EQ: What are prime and composite numbers?

10. EQ: What are prime and composite numbers?
Practice
Follow along as we complete the Buckle Down Book Prime and Composite Numbers worksheet.
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Click on the blue highlighted words. This will open a new document for the smart board. Pass out the Buckle Down Book Prime and Composite numbers worksheet. Have students follow along as you do a few problems on the board. Call on students to help answer questions. Have them to go to the board if you wish.
EQ: What are prime and composite numbers?

11. EQ: What are prime and composite numbers?
Classwork
Complete the IIII Minutes to IV Minutes packet on prime and composite numbers.
I will be collecting this for a grade.
If you need help with any part of this packet, please see me ASAP.
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Click on the blue highlighted words to access the assignments using the smart board. You may wish to break the class into cooperative groups and work with groups of students at a time. Pass out the Packet and have students work Independently in class.
EQ: What are prime and composite numbers?

12. EQ: What are prime and composite numbers?
How will you remember?
How will you remember the difference between a prime number and a composite number?
Write your idea on a sticky note.
Be sure to put your name on it!
Stick your idea to the door before you leave!
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After students have time to complete the classwork, have them go back to their seats to complete the summary on this slide. Have students brainstorm ways to remember the difference between a prime and composite number. Give each student a sticky note to write down their ideas. Have students stick their ideas to the door as they leave.
EQ: What are prime and composite numbers?

13. How do you change a composite number to a prime number?
What are your ideas?
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Activating Strategy: Write the question on the white board. As students enter the room, have them write 1 idea on the white board. Do this before they sit down to work on the warm up.
When it’s time, read their ideas out loud.
EQ: How is the prime factorization of a number determined?

14. EQ: How is the prime factorization of a number determined?
Key Vocabulary
Re-writing
Prime Factorization: Expressing a composite number as the product of prime numbers.
Example:
the prime factorization of 63 is 3 x 3 x 7= 32 x 7.
To multiply
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Construct Models: Students will write the definition of the word prime factorization in their notebooks.
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15. EQ: How is the prime factorization of a number determined?
Factor Tree
Steps to find Prime Factorization:
Step 1: Write the composite number.
Step 2: Find two numbers whose product is the composite and write them directly below.
Step 3: Circle any prime numbers.
Step 4: repeat steps 2-3 for the new composite numbers.
Step 5: Write all prime numbers as a product in order from least to greatest.
Step 6: Re-write using exponents
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Construct Models: Steps to using a factor tree
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16. EQ: How is the prime factorization of a number determined?
Examples
1. Find the prime factorization of 36.
Draw a factor tree
Step1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6: 36
2 x 2 x 3 x 3
22 x 32
No primes
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Construct Models: Examples
EQ: How is the prime factorization of a number determined?

17. EQ: How is the prime factorization of a number determined?
Examples
2. Find the prime factorization of 255.
Draw a factor tree
Step1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
255
3 17
3 x 5 x 17
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No need for exponents
EQ: How is the prime factorization of a number determined?

18. EQ: What are prime and composite numbers?
Practice
Follow along as we complete the Buckle Down Book Prime Factorization worksheet.
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Shape: Practice finding the prime factorization of numbers with the students.
Make sure all primes are circled
Think about the difference between a prime and composite number.
A composite number cannot be in the prime factorization
You do NOT need to multiply the numbers together at the end because you will get the number you started with.
EQ: What are prime and composite numbers?

19. EQ: What are prime and composite numbers?
Classwork
Complete the Prime factorization worksheet
I will be collecting this for a grade.
If you need help with any part of this paper, please see me ASAP.
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EQ: What are prime and composite numbers?

20. Solve the following problem
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Use a strategy: Draw a picture
Is there an easier way to solve the problem?
Yes, use the factor of 27 and 45!
Activating Strategy:
Have students work with a partner or in a group to answer the problem. Students should use the word problem solving strategy, draw a picture, to solve the problem. Have a few pairs of students share their answers.
Hook:
Tell the students that there is an easier way to solve the problem by finding common factors.
EQ: How is the greatest common factor of two or more numbers found?

21. EQ: How is the greatest common factor of two or more numbers found?
Key Vocabulary
Factor: A number that divides into a whole number evenly.
Example:
5 is a factor of 30.
Greatest Common Factor (GCF): The greatest of the common factors of two or more numbers.
The GCF of 24 and 30 is 6.
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biggest
same
Number that divides evenly
Construct Meaning:
Students will take notes on key vocabulary for this essential question. Students will write down the key vocabulary words and the examples.
Have students “dissect” the definitions by looking for synonyms of difficult or confusing words.
Ask students what the following words mean before advancing the slide:
Greatest-biggest
Common-the same
Factor- number that divides evenly into another number
EQ: How is the greatest common factor of two or more numbers found?

22. EQ: How is the greatest common factor of two or more numbers found?
To Find GCF
Make a t-chart
List all of the factors of each number
Find the factors that are the same
Circle the largest of the common factors
There will always be a GCF
it may be 1
Example: GCF of 2 and 3 is 1.
it may be the smallest number
Example: GCF of 4 and 8 is 4.
It will never be bigger than the largest number
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Construct Meaning:
Students will take notes.
EQ: How is the greatest common factor of two or more numbers found?

23. EQ: How is the greatest common factor of two or more numbers found?
Examples
1. Find the GCF of 27 and 45
27: 1, 3, 9, 27
45: 1, 3, 5, 9, 15, 45
Common Factors: 1, 3, 9
GCF: 9
Therefore, the greatest number of flag line and drill team members in each row is 9.
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Shape:
Remind students to use the divisibility rules to find the factors.
Also, work from small to big and meet in the middle. Then, work backwards once you find the factors in the middle.
EQ: How is the greatest common factor of two or more numbers found?

24. EQ: How is the greatest common factor of two or more numbers found?
Examples
2. Find the GCF of 32, 48 and 80
32: 1, 2, 4, 8, 16, 32
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
80: 1, 2, 4, 5, 8, 10, 16, 20, 40,80
Common Factors: 1, 2, 4, 8, 16
GCF: 16
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Shape:
Continue to take notes
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25. EQ: What are prime and composite numbers?
Practice
Follow along as we complete the Buckle Down Book Greatest Common Factor worksheet.
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Internalize: Click on the blue highlighted words. This will open a new document for the smart board. Pass out the Buckle Down Book Greatest Common Factors worksheet. Have students follow along as you do a few problems on the board. Call on students to help answer questions. Have them to go to the board if you wish.
EQ: What are prime and composite numbers?

26. EQ: How is the greatest common factor of two or more numbers found?
Ticket out The Door
On your index card
1. Explain how to find the GCF of 12 and 18.
2. Tell how the GCF of two numbers should be one of the two numbers.
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Summarizing Strategy:
Pass out an index card or scrap paper to each student. Have them complete the Ticket out the door before they leave the classroom. Collect their work.
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27. EQ: How is the least common multiple of two or more numbers found?
Solve the Problem
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Activating Strategy:
Break the class up into groups of no more than 4. Have them try to solve this problem without giving them any hints. It should be difficult for them to solve. Give them no more than 5 minutes to attempt to solve the problem.
Bring students back together as a whole group. Have a few groups explain what they did to solve the problem. Then, advance the slide to give them a hint as what to do. This will link the activity to today’s lesson.
Is there an easier way to solve this problem?
Yes! Find the multiples!
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28. EQ: How is the least common multiple of two or more numbers found?
Key Vocabulary
Multiple: The product of the number and any whole number.
Example:
A multiple of 4 is 24.
Least Common Multiple (LCM): The least of the common multiples of two or more numbers.
The LCM of 2 and 3 is 6.
multiply
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smallest
same
product
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29. EQ: How is the least common multiple of two or more numbers found?
To Find LCM
Make a t-chart
List the first few multiples of each number
Circle the first multiple they have in common
There will always be an LCM
It may be the product of the two numbers, but never bigger than the product
Example: The LCM of 5 and 8 is 40
It may be the larger number
Example: The LCM of 4 and 8 is 8
It will never be smaller than the smaller number.
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30. EQ: How is the least common multiple of two or more numbers found?
Examples
1. Find the LCM of 4 and 7
4: 4, 8, 12, 16, 20, 24, 28
7: 7, 14, 21, 28
LCM: 28
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EQ: How is the least common multiple of two or more numbers found?

31. EQ: How is the least common multiple of two or more numbers found?
Examples
2. Find the LCM of 10, 16, and 8.
10: 10, 20, 30, 40, 50, 60, 70, 80
16: 16, 32, 64, 80
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
LCM: 80
So, the least amount of packages Joe needs to buy to have the same amount of cups, napkins, and plates is 8 packages of plates, 5 packages of napkins, and 10 packages of cups.
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EQ: How is the least common multiple of two or more numbers found?

32. EQ: How is the least common multiple of two or more numbers found?
Practice
Follow along as we complete the Buckle Down Book Least Common Multiple worksheet.
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Internalize: Click on the blue highlighted words. This will open a new document for the smart board. Pass out the Buckle Down Book Greatest Common Factors worksheet. Have students follow along as you do a few problems on the board. Call on students to help answer questions. Have them to go to the board if you wish.
EQ: How is the least common multiple of two or more numbers found?

33. EQ: How is the least common multiple of two or more numbers found?
Write a letter
Write a letter to an absent student explaining how to find the LCM of two or more numbers.
Be sure to include an example as well as a written explanation of the steps you used to find LCM.
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Summarizing Strategy:
Pass out a piece of lined paper to each student and have them write a letter to an absent student explaining how to find the LCM of two or more numbers. They must include an example in their letter.
EQ: How is the least common multiple of two or more numbers found?

34. Key Vocabulary
Upside-Down Division: A strategy to find the prime factorization, GCF, and LCM of two or more numbers using division.