Transcript d) GCF

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Factor - A whole number or variable expression
that divides evenly into a given whole
number or variable expression.
List all the positive factors of the following.
20
40
Why do you
1 20
1 40
think I always
2 20
Make 2 10
start with one?
4
5
4
10
a list!
5 8
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Making a list can be helpful to keep track of data
and to spot any missing data.
To find factors of a number make a list starting
with the lowest possible factor which is 1.
We start with 1 and work our way up. We know
we didn’t miss any factors because our list is
organized.
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When two numbers have the same
factor it is called a common factor.
Can you think of a common factor
for 12 and 6?
2, 3 or 6
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GCF- Greatest Common Factor - Largest
number that divides evenly into a given
set of numbers.
It is useful to know this for reducing
fractions.
There are two ways to find the GCF
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Method # 1 List all the factors of both numbers.
Then find the greatest common factor.
Ex.
Factors of 12
1 x 12
2x 6
3x 4
Factors of 30
1 x 30
2 x 15
3 x 10
5x 6
Common Factors are 1,2,3,6 GCF= 6
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Make a List
60
1 60
2 30
3 20
4 15
5 12
6 10
84
1 84
2 42
3 28
4 21
6 14
7 12
GCF = 12
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This method
is only
useful if
both
numbers are
small
Method #1 is great, but you have to list
all of the factors for both numbers!
This can sometimes take a while!
That’s why there is
Method # 2
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Find the prime factorization of the two numbers.
Then multiply their common factors.
30
12
2
2 15
6
2
3
3
2 23
5
2  3 5
Factors the 2 numbers have in common are: 2 and 3
Multiply the common factors. GCF: 2 x 3 = 6.
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Prime Factorization
60
84
2
2
30
15
2
3
42
21
2
5
3
7
2  2  3 5 2  2  3 7
GCF  2  2  3
GCF = 12
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Prime Factorization
24
20
2 10
2
2 12
5
2 25
6
2
2
3
2 2 23
GCF  2  2  4
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Watch and see why it is important to know GCF!
The GCF is used to reduce or to simplify fractions.
32 2 16 2 8 2 4 2 2




48 2 24 2 12 2 6 2 3
32 16 2

48 16 3
GCF
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Simplify or Reduce This Fraction
12
6
2
÷ =
18
6
3
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Take Out Your Study Guide!!!
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#7
GCF, Make a List Method #1
GCF is the largest number that is a factor of 2 numbers.
It is useful to know this for reducing fractions.
Step 1: List all the factors of both numbers.
Step 2: Then find the greatest common factor.
Ex.
Factors of 12
1 x 12
2x 6
3x 4
Factors of 30
1 x 30
2 x 15
3 x 10
5x 6
Common Factors are 1,2,3,6 GCF= 6
This method is only useful if both numbers are small
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#8
Find the prime factorization of the 2 numbers.
Step 2: Then multiply their common factors.
Step 1:
30
12
2
2 15
6
2
3
3
2 23
5
2  3 5
Factors the 2 numbers have in common are: 2 & 3
Multiply the common factors. GCF  2  3  6
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