Question

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

Answer 1

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=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

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

Explanation:

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`