Greatest Common Factor Least Common Multiple Prime Factorization 6 th Grade Mathematics Miss Quimby’s Class
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Greatest Common FactorLeast Common MultiplePrime Factorization
6th Grade Mathematics
Miss Quimby’s Class
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?
What do these three pictures have in common?
The are all prime!
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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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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. Example:
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?
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!
EQ: What are prime and composite numbers?
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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 4 + 2 + 8 = 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 2 + 7 + 3 + 6 = 18. Since 18 ÷ 9 = 2, 2,736 is divisible by 9.
EQ: What are prime and composite numbers?
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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!
EQ: What are prime and composite numbers?
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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.
EQ: What are prime and composite numbers?
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Practice
Follow along as we complete the Buckle Down Book Prime and Composite Numbers worksheet.
EQ: What are prime and composite numbers?
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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.
EQ: What are prime and composite numbers?
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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!
EQ: What are prime and composite numbers?
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How do you change a composite number to a prime number? What are your ideas?
EQ: How is the prime factorization of a number determined?
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Key Vocabulary
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
Re-writing
EQ: How is the prime factorization of a number determined?
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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
EQ: How is the prime factorization of a number determined?
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Examples
1. Find the prime factorization of 36. Draw a factor tree
Step1: Step 2: Step 3: Step 4: Step 5: Step 6:
36
4 9
2 2 3 3
2 x 2 x 3 x 3
22 x 32
No primes
EQ: How is the prime factorization of a number determined?
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Examples
2. Find the prime factorization of 255. Draw a factor tree
Step1: Step 2: Step 3: Step 4: Step 5: Step 6:
255
5 51
3 17
3 x 5 x 17
No need for exponents
EQ: How is the prime factorization of a number determined?
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Practice
Follow along as we complete the Buckle Down Book Prime Factorization worksheet.
EQ: What are prime and composite numbers?
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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?
Solve the following problem
Use a strategy: Draw a picture Is there an easier way to solve the problem?
Yes, use the factor of 27 and 45!
EQ: How is the greatest common factor of two or more numbers found?
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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. Example:
The GCF of 24 and 30 is 6.
biggest
EQ: How is the greatest common factor of two or more numbers found?
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sameNumber that divides evenly
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
EQ: How is the greatest common factor of two or more numbers found?
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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.
EQ: How is the greatest common factor of two or more numbers found?
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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
EQ: How is the greatest common factor of two or more numbers found?
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Practice
Follow along as we complete the Buckle Down Book Greatest Common Factor worksheet.
EQ: What are prime and composite numbers?
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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.
EQ: How is the greatest common factor of two or more numbers found?
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Solve the Problem
Is there an easier way to solve this problem? Yes! Find the multiples!
EQ: How is the least common multiple of two or more numbers found?
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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. Example:
The LCM of 2 and 3 is 6.
multiply
same
product
smallest
EQ: How is the least common multiple of two or more numbers found?
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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.
EQ: How is the least common multiple of two or more numbers found?
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Examples
1. Find the LCM of 4 and 7
4: 4, 8, 12, 16, 20, 24, 28
7: 7, 14, 21, 28
LCM: 28
EQ: How is the least common multiple of two or more numbers found?
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Examples
2. Find the LCM of 10, 16, and 8.
10: 10, 20, 30, 40, 50, 60, 70, 8016: 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.
EQ: How is the least common multiple of two or more numbers found?
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Practice
Follow along as we complete the Buckle Down Book Least Common Multiple worksheet.
EQ: How is the least common multiple of two or more numbers found?
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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.
EQ: How is the least common multiple of two or more numbers found?
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Key Vocabulary
Upside-Down Division: A strategy to find the prime factorization, GCF, and LCM of two or more numbers using division.
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