Gcf

Brian P.

asked • 09/12/15

What is a easy way of finding the GCF?

I have had many ways,but is there a fast and easy method of doing so?

Yohan C.

Hi Brian,
 
Make your own "double-digit" multiplication table and memorize them.  Most people memorize their multiplication tables up to 9 (sometimes 12).  I'm talking about all 10s, 20s, 30s, 40s, and beyond because GCF stands for Greatest Common Factor.  The keyword is GREATEST (Biggest).
 
Or draw "tree diagram" and find all the common factors and circle the common factors from each set.  Sometimes, you don't have to go down to smallest number because you are trying to find the GREATEST.
 
For example:
 
24, 8, 36
 
24  =  1, 2, 3, 4, 6, 8, 12, 24     8 = 1, 2, 4, 8        36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
 
18, 36, 60
 
18 = 1, 2, 3, 6, 9, 18        36 = 1, 2, 3, 4, 6, 9, 12, 18, 36       60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
 
There is no trick to this.
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09/12/15

Brian P.

Thanks for the answer! :)
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09/12/15

1 Expert Answer

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David W. answered • 09/12/15

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A very easy method is to simply list the prime factors of each number, then collect the factors common to all.
 
For example, the prime factors of:
   18   =   2 * 3 * 3
   24   =   2 * 2 * 2 * 3
There is 2 and a 3 in common, so the CGF (Greatest Common Factor) is 2 * 3 = 6.  (Note:  6 divides evenly into both 18 and 24; it is the largest number that does so).
 
For more than two values, the prime factors must appear in all of the numbers.
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Brian P.

Thanks for explaining that to me :)!
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09/12/15

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