Greatest Common Factor (GCF)
Objective
Know how to find the GCF of a fraction
Example
Find the GCF of the following fraction
5
21
24
Answer: 3
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Explanation
Greatest Common Factor (GCF)
Greatest: biggest
Common: For both
Factor: A number we can divide by without a remainder
You've learned how to figure out whether or not a number is a factor. Now, our goal is to figure out which of those factors is the biggest. This can take forever, because you have to check every single number to see if it is a factor.
If you've learned the shortcuts from the previous level, you'll be off to a good start. With bigger numbers, watch out for factors like 15, 20, 25, 30, 50, and 100
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Examples
Example 1
Find the GCF of the following fraction
18
12
Is 1 a common factor? yes
Is 2 a common factor? yes
Is 3 a common factor? yes
Is 4 a common factor? no
Is 5 a common factor? no
Is 6 a common factor? yes
Is 7 a common factor? no
Is 8 a common factor? no
Is 9 a common factor? no
Is 10 a common factor? no
Is 11 a common factor? no
Is 12 a common factor? no
Answer: 6
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Example 2
Find the GCF of the following fraction
7
30
90
Rather than checking everything up to 30, lets think about it. Already we can see that 10 is a common factor because both numbers end it 0. Lets reduce the whole thing by 10 and see what's left
30 ÷ 10 = 3
90 ÷ 10 = 9
I can see 3 that is the GCF of 3 and 9.
So to find the GCF of the original fraction, just multiply our new GCF (3) with the number we reduced by (10)
3 x 10 = 30
Answer: 30
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Practice your skills
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Ready?