Download 8-1 2014.notebook

8­1 2014.notebook
October 30, 2014
Table of Contents
8­1 Factors and Greatest Common Factors.......................#
(or Goals)
Write factors of numbers
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Some Numbers have many factors.
360 has the following factors:
Note: 1,2,3,4,5,6,8,9,10,12,15,18,20,
When you are asked to list factors of numbers, 24,30,36,40,45,60,72,90,120,180,360
list all the possible factors. Doing so will help you determine
the Greatest Common Factor Some Numbers only have two factors.
between TWO numbers.
13 has only two factors 1 and 13
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How can
you
check
your
answer?
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List the factors of each number.
a. 40
b. 33
c. 49
d. 19
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8­1 2014.notebook
A "How To" Guide to finding a GCF?
1. List the factors of each number.
2. Circle the LARGEST common factor.
3. Write the answer in the following form:
GCF(expression 1, expression 2,...) = GCF
October 30, 2014
Example 1 Find the GCF of the following numbers: 30 and 55
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 55: 1, 5, 11, 55,
Answer:
GCF(30,55)=5
Nov 5­10:09 AM
Can the
GCF of
two
numbers
be one of
the
numbers?
Your Turn:
Oct 29­12:30 PM
We can also find the Greatest Common Factor (GCF) of other "numbers". Look at the following Monomials
3x3 and 6x2 have a GCF too.
Watch
We will follow the same process we did for numbers but list all the variables too.
Factors of 3x3: 1, 3 and x, x, x
Factors of 6x2: 1, 2, 3, 6 and x, x
Answer:
GCF(3x3, 6x2)=3x2
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A "How To" Guide to finding a GCF?
Example 2 1. List the factors of each number.
Find the GCF of the following numbers: 18x2y and 24xy3
2. Circle the LARGEST common factor.
3. List the factors of each variable.
4. Circle the common variables.
5. Write the answer in the following form:
Factors of 18x2y: 1, 2, 3, 6, 9, 18, x, x, y,
Factors of 24xy3: 1,2, 3, 4, 6, 8, 12, 24, x, y, y,y Answer:
GCF(18x2y,24xy3)=6xy
GCF(expression 1, expression 2,...) = GCF
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8­1 2014.notebook
October 30, 2014
write this down in your notes...
Your Turn:
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A Special Case
Example 3 Find the GCF of the following numbers: 17x2z and 4y3w2
What
happens if
monomials
do not
contain the
same
variable?
Factors of 17x2z: 1, 17, x, x, z,
Factors of 4y3w2: 1, 2, 4, y, y, y, w, w The only factor they have in common is 1
Answer:
GCF(17x2z,4y3w2)=1
Oct 29­2:12 PM
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What if there are three monomials?
Example 4 Do the same thing!
Find the GCF of the following numbers: 10x2z and15xy2 and 25xy
Factors of 10x2z: 1, 2, 5, 10, x, x, z,
Factors of 15xy2: 1, 3, 5, 15, x, y, y Factors of 25xy: 1, 5, 25, x, y, Answer:
GCF(10x2z,15xy2,25xy)=5x
Oct 29­2:12 PM
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Assignment: p. 527 #17­24 List Factors
25­35 all 60­64 all
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