4­2 GCF.notebook
November 11, 2013
pg 183­184 #'s 1­10, 30­34
4­2: Greatest Common Factor
Please have your homework assignment out on your desk.
You have 4 minutes to complete the problems below.
5.
1. Prime
9. 24 x x x x
2. Composite
10. 11 x g x g x g
3. Prime
30. 22 x 5 x p x q
4. 12 ways
31. 2 x 17 x j x k x m
5. 2 x 17
32. 72 x y x y
6. 2 x 3 x 5
33. 22 x 13 x g x h x h
7. 22 x 3
34. 24 x 3 x a x a x b x b 8. 2 x 5 x a x c
Nov 18­7:48 AM
x
Nov 3­4:50 PM
Definition:
4­2: Greatest Common Factor
Main Idea: Find the greatest common
factor of two or more numbers.
Vocabulary:
• Venn diagram ­ A diagram that uses
overlapping circles to show how elements
among sets of numbers or objects are
related
• greatest common factor (GCF) ­ The
greatest of the common factors of two or
more numbers.
The Greatest Common Factor is the greatest number
that is a factor of two or more numbers.
Example: The GCF of 6 and 8 =
Mar 8­4:57 PM
2
Mar 8­5:01 PM
There are several ways to find the
GCF between two numbers.
Another way to find the GCF
between two numbers is to use a
factor tree.
One way that you have learned is just to list the factors.
12
Factors of 12 = (1, 2, 3, 4, 6, 12)
24
Factors of 24 = (1, 2, 3, 4, 6, 8, 12, 24)
Then, you circle the common factors and find the largest one which is
the........GREATEST COMMON FACTOR!
12
Answer
What is the GCF of 12 and 24?
2
6
4
4
3
2
2
2 X 2 X 3 = 12
2
2
3
2 X 2 X 2 X 3 = 24
GCF = 2 x 2 x 3 = 12
Mar 8­5:16 PM
Mar 8­5:16 PM
1
4­2 GCF.notebook
November 11, 2013
Now it is time to make your
own birthday cakes!
Another way to find the GCF is called the
Birthday Cake Factorization!
First, make a small list of prime numbers for reference..
Second, build the cake using only
prime numbers as divisors.
Third, write the equation.
2
2
Watch this youtube video!
2
The first step is to make a birthday cake for a given number
using prime factors......
2
Mar 8­5:16 PM
2, 3, 5, 7, 11
1
2
4
8
Prime Factorization
16
2 x 2 x 2 x 2 = 16
Mar 8­5:25 PM
12
ANOTHER EXAMPLE: Do a Prime Factorization for 12
24
First, make a small list of prime numbers for reference..
2, 3, 5, 7, 11
Second, build the cake using only
prime numbers as divisors.
3
2
2
12
1
Third, write the equation.
1
3
GCF
1
=
12
Prime Factorization
12
2 2
2 4
3 3
6
2 6
2 8
2 12
3 24
2 x 2 x 3 = 12
Mar 8­5:25 PM
18
GCF
2
2 x2x3
24
=
Mar 8­4:44 PM
Mar 8­4:44 PM
48
GCF
56
=
Mar 8­4:44 PM
2
4­2 GCF.notebook
November 11, 2013
25
45
16x2 and 4x
GCF
=
Mar 8­4:44 PM
Nov 3­6:04 PM
Assignment:
p. 188­189, # 13­20 ,23­29,
30xy and 12xyz
Nov 3­6:04 PM
Nov 18­7:47 AM
3
Attachments
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