What is the greatest common factor of 8, 12 and 24? Provide an explanation of how the find greatest common factor.

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Answer 1 · 2018-02-08T04:50:51

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

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

$8=color(blue)(2xx2)xx2$

$12=color(blue)(2xx2)" "xx3$

$24=color(blue)(2xx2)xx2xx3$

Now, look for the factors that can be found in all three expressions.
This is just $color(blue)(2xx2)$

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

Answer 2 · 2018-02-11T09:19:48

$gcf(8,12,24)=4$

Another approach

List all the factors and pick out the common ones

factors $" "8:{color(red)(1,2,4),8}$

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

factors $" "24:{color(red)(1,2),3,color(red)(4),6,8,12,24}$

common factors $" "{1,2,4}$

$gcf(8,12,24)=4$