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?