# What is greatest common factor of 8," "12" and " 24?

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sjc Share
Feb 11, 2018

$g c f \left(8 , 12 , 24\right) = 4$

#### Explanation:

Another approach

List all the factors and pick out the common ones

factors$\text{ } 8 : \left\{\textcolor{red}{1 , 2 , 4} , 8\right\}$

factors" "12;{color(red)(1,2),3,color(red)(4),6,12}

factors$\text{ } 24 : \left\{\textcolor{red}{1 , 2} , 3 , \textcolor{red}{4} , 6 , 8 , 12 , 24\right\}$

common factors$\text{ } \left\{1 , 2 , 4\right\}$

$g c f \left(8 , 12 , 24\right) = 4$

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Feb 13, 2018

The greatest common factor of these numbers is 4.
How you determine this is explained below

#### Explanation:

To find greatest common factor, write each number as the product of its prime factors:

$8 = \textcolor{b l u e}{2 \times 2} \times 2$

$12 = \textcolor{b l u e}{2 \times 2} \text{ } \times 3$

$24 = \textcolor{b l u e}{2 \times 2} \times 2 \times 3$

Now, look for the factors that can be found in all three expressions.
This is just $\textcolor{b l u e}{2 \times 2}$

This product is the greatest common factor. ($4$ in this case.)

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