Transcript Factors and Multiples - JJ Daniell Middle School

Warm-Up #3
Use the following terms to describe your
number: prime factorization and
exponential form. Underline these terms in
your journal.
Be sure to give an accurate description with
numerical justifications.
If a room’s area is 60 square feet, what
are the possible combinations of
dimensions (length and width)?
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What is it asking?
Name all of the factor facts for 60.
1 x 60 It could be 1 foot long and 60 feet wide.
2 x 30 It could be 2 foot long and 30 feet wide.
3 x 20 It could be 3 foot long and 20 feet wide.
4 x 15 It could be 4 foot long and 15 feet wide.
5 x 12 It could be 5 foot long and 12 feet wide.
6 x 10 It could be 6 foot long and 10 feet wide.
4-2 Factors
Insert Lesson
and Prime
TitleFactorization
Here
Lesson Quiz
List all the factors of each number.
1. 22
1, 2, 11, 22
2. 40
1, 2, 4, 5, 8, 10, 20, 40
3. 51
1, 3, 17, 51
Write the prime factorization of each number.
4. 32
25
5. 120
23  3  5
Course 1
Factors and Multiples
Number Theory GONE WILD!
Factors “Fit” into Families
Multiples Multiply like
Rabbits!
What am I Learning Today?
GCF
How will I show that I learned it?
Show how prime factorization can be used
to find GCF
Determine the GCF between two sets of
data
Vocabulary
Common factor: Factors shared by two
or more whole numbers
Greatest Common Factor (GCF): The
largest number that divides two or
more numbers evenly.
Questions
Answers
What are common
factors?
Factors shared by two or more whole
numbers
What is the largest of the
common factors?
The greatest common factor, or GCF.
How do I find the GCF?
Using the list method or the ladder
How do I use the list
method?
1. List all the factor pairs for those two numbers.
2. Circle the largest factor that they share.
List the GCF for 28 and 42
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
How do I use the ladder
method?
The GCF of 28 and 42 is 14.
1. Begin with a factor that divides into each
number evenly. Does not have to be prime.
2. Keep dividing until there are no more common
factors.
3. Find the product of the numbers you divided by
(GCF IS ON THE LEFT).
Questions
Using the ladder, find the
GCF for 40 and 16.
Answers
2
40
16
2 20 8
2 10 4
5 2
2•2•2= 8
The GCF of 40 and 16 is 8
Find the Greatest Common Factor
Use BOTH the list and ladder method in order to
check your answers.
GCF of 32 and 24
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
GCF of 54 and 36
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
2
32
24
2 16
12
2
2
8
6
4
3
54
3
36
27
18
3 9
3
6
2
Find GCF using a Venn
Diagram
Paired Discussion
Turn to a partner and discuss the following:
What is the GCF of two prime numbers?
Explain.
Each prime number
only has two factors, so
they can ONLY share
the number ONE.
GCF Problem
Solving
How can you tell if a word problem
requires you to use Greatest
Common Factor?
If it is a GCF Problem
You are probably being asked:
• Do we have to split things into smaller
sections?
• Are we trying to figure out how many
people we can invite?
• Are we trying to arrange something into
rows or groups?
GCF Example: Applying what
we have learned…
Samantha has two pieces of cloth. One piece is 72
inches wide and the other piece is 90 inches wide.
She wants to cut both pieces into strips of equal
width that are as wide as possible. How wide should
she cut the strips?
• K: The pieces of cloth are 72 and 90 inches wide.
• W: How wide should she cut the strips so that they
are the largest possible equal lengths.
• L: This problem can be solved using Greatest
Common Factor because we are cutting or “dividing”
the strips of cloth into smaller pieces (factor) of 72
and 90.
When is this useful?
Dr. Doyle’s band students have been invited to
march in a parade along with another school.
Since one band marches directly behind
another, all the rows must have the same
number of students. Dr. Doyle had 36
students and the other band has 60 students.
What is the greatest number
of students who can be in
each row?
12 students per row
Consumer Application
Peter has 18 oranges and 27 pears. He wants to
make fruit baskets with the same number of
each fruit in each basket. What is the greatest
number of fruit baskets he can make?
HINT: The answer will be the greatest number of
fruit baskets 18 oranges and 27 pears can form so
that each basket has the same number of oranges,
and each basket has the same number of pears.
The GCF of 18 and 27 is 9.
Question #1
Mrs. Evans has 120 crayons and 30
pieces of paper to give to her
students. What is the largest
number of students she can have in
her class so that each student gets
an equal number of crayons and an
equal number of paper?
GCF: 30 students
Question #2
Rosa is making a game board that is 16
inches by 24 inches. She wants to use
square tiles. What is the largest tile she
can use?
GCF: 8 inch tile
Question #3
I am planting 50 apple trees and 30 peach
trees. I want the same number and type of
trees per row. What is the maximum
number of trees I can plant per row?
GCF: 10 trees
Ticket Out The Door
Find the GCF for the following problems.
1. 12 and 15
2. 16, 28, and 48