Download EQ: What are prime and composite numbers?

Greatest Common Factor
Least Common Multiple
Prime Factorization
6th Grade Mathematics
Miss Quimby’s Class
Table of Contents
 Lesson 1: What are prime and composite
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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?
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What do these three pictures have in
common?
The are all prime!
Key Vocabulary Page
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 On the top of the next clean page write:
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GCF/LCM/Prime Factorization Vocabulary
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Create a word column and a definition column
Paperclip the next 2 pages together.
Keep track of all new vocabulary on these
pages.
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At the end of the unit you will have a key
vocabulary list to use to study.
Key Vocabulary
 Prime Number: Any whole number, greater than 1,
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that can only be divided evenly by 1 and itself.
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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.
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Example:
 4 can be divided by 4, 1, and 2
 4÷4=1
 4÷1=4
 4÷2=2
With no remainder
EQ: What are prime and composite numbers?
Divisibility Rules
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 To quickly tell if a number is prime or
composite use the following rules:
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A number is divisible by:
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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.
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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.
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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.
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Since 18 ÷ 9 = 2, 2,736 is divisible by 9.
EQ: What are prime and composite numbers?
Prime vs. Composite
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 Every number is either prime or composite.
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Use the divisibility rules
 Ask yourself, “Is there anything that can
divide evenly into this number other than itself
and 1?”
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Yes- composite.
No- prime.
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ODD does NOT equal Prime!
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EQ: What are prime and composite numbers?
Examples
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 1. Is 18 a prime or composite number?
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Does anything other than 1 and 18 divide
evenly into 18?
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Yes, 2, 3, 6, and 9.
 So, 18 is composite.
 2. Is 29 a prime or composite number?
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Does anything other than 1 and 29 divide
evenly into 29?
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No, only 1 and 29.
 So, 29 is prime.
EQ: What are prime and composite numbers?
Practice
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 Follow along as we complete the Buckle
Down Book Prime and Composite Numbers
worksheet.
EQ: What are prime and composite numbers?
Classwork
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 Complete the IIII Minutes to IV Minutes
packet on prime and composite numbers.
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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?
How will you remember?
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 How will you remember the difference
between a prime number and a composite
number?
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Write your idea on a sticky note.
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Be sure to put your name on it!
Stick your idea to the door before you leave!
EQ: What are prime and composite numbers?
How do you change a composite
number to a prime number?
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 What are your ideas?
EQ: How is the prime factorization of a number determined?
Key Vocabulary
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 Prime Factorization: Expressing a
composite number as the product of prime
numbers.
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Example:
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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?
Factor Tree
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 Steps to find Prime Factorization:
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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?
Examples
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 1. Find the prime factorization of 36.
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Draw a factor tree
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Step1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
36
4
2
9
2
3
No primes
3
2x2x3x3
22 x 3 2
EQ: How is the prime factorization of a number determined?
Examples
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 2. Find the prime factorization of 255.
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Draw a factor tree
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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?
Practice
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 Follow along as we complete the Buckle
Down Book Prime Factorization worksheet.
EQ: What are prime and composite numbers?
Classwork
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 Complete the Prime factorization worksheet
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I will be collecting this for a grade.
If you need help with any part of this paper,
please see me ASAP.
EQ: What are prime and composite numbers?
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Solve the following problem
 Use a strategy: Draw a picture
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Is there an easier way to solve the problem?
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Yes, use the factor of 27 and 45!
EQ: How is the greatest common factor of two or more numbers found?
Key Vocabulary
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 Factor: A number that divides into a whole
number evenly.
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Example:
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5 is a factor of 30.
 Greatest Common Factor (GCF): The
greatest of the common factors of two or
more numbers.
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Example:
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biggest
The GCF of 24 and 30 is 6.
same
Number that divides evenly
EQ: How is the greatest common factor of two or more numbers found?
To Find GCF
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 Make a t-chart
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List all of the factors of each number
Find the factors that are the same
Circle the largest of the common factors
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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?
Examples
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 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
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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?
Examples
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 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?
Practice
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 Follow along as we complete the Buckle
Down Book Greatest Common Factor
worksheet.
EQ: What are prime and composite numbers?
Ticket out The Door
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 On your index card
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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?
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Yes! Find the multiples!
EQ: How is the least common multiple of two or more numbers found?
Key Vocabulary
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 Multiple: The product of the number and any
whole number.
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Example:
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multiply
A multiple of 4 is 24.
 Least Common Multiple (LCM): The least of
the common multiples of two or more
numbers.
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Example:
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The LCM of 2 and 3 is 6.
smallest
product
same
EQ: How is the least common multiple of two or more numbers found?
To Find LCM
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 Make a t-chart
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List the first few multiples of each number
Circle the first multiple they have in common
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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?
Examples
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 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?
Examples
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 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.
EQ: How is the least common multiple of two or more numbers found?
Practice
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 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?
Write a letter
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 Write a letter to an absent student explaining
how to find the LCM of two or more numbers.
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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?
Key Vocabulary
 Upside-Down Division: A strategy to find the
prime factorization, GCF, and LCM of two or
more numbers using division.