How to find the Greatest Common Factor Easily

What is the Greatest Common Factor?

Greatest Common Factor Practice Problems Quiz

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Watch our free video on how to find GCF. This video shows how to solve problems that are on our free Greatest Common Factor worksheet that you can get by submitting your email above.

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Video Transcript:

This video is about how to find the greatest common factor. You can get the gcf worksheet used in this video for free by clicking on the link in the description below.

The greatest common factor definition in math is the largest common factor that goes into two separate numbers. Now factors are just numbers that you can multiply together to make another number. For example, if we were to take a number like the number 12 and we were to break it down into factors that were prime numbers only, this would be called prime factorization. We’re going to factor 12 into a list of prime factors that when multiplied together will equal 12.

The first prime factor I’m going to factor out of this 12 is 2 and I’m using 2 because it’s an even number and I know that 2 will have to go into 12 because it’s even. Now we have to figure out 2 times what is 12, 2 times 6 is 12. We cannot break 2 down anymore because it’s a prime factor nothing else goes into it except itself and the number 1. But we can break 6 down into prime factors. I can break 6 down into 2 times 3 and now we have a list of prime factors because each number is a prime number. 2 and 3 are all prime which means that we are done with our factorization. You could say 12 broken down into prime factorization is going to be 2 times 2 times 3 and I’m going to write it like this 2 times 2 times 3 and this is what we’re going to use to figure out the greatest common factor.

If we were given a greatest common factor example like finding the greatest common factors between 50 and 20, what we could do is we could take each number and break it down into a list of prime factorization. You could do this a couple different ways. I’m going to use the factor tree method that I just showed you. The first number I’m going to do is I’m going to take the number 50 and I’m going to break it down into prime factors. Now 50 is an even number so I know that 2 automatically has to go into 50. 2 times 25 is 50. Then if I look 25 can be broken down again into prime factors and 25 in the prime factors is going to be 5 times 5. Now I have my list of prime factors which in this case is 2 times 5 times 5. I can do the same thing for the number 20. I’m going to break down 20. 20 is an even number so I’m going to break it down by 2 and then 2 times 10 is 20 and then I can break 10 down again into 2 times 5. Now I know that I’m done because it’s only prime numbers that I have left over.

Now i’m going to take 50 and 20 and I’m going to list them both out by their list of prime factors 50 is 2 times 5 times 5 and 20 is 2 times 2 times 5. In order to find the greatest common factor, you’re going to take the pairs of prime factors that both 50 and 20 have in common. I’m going to use this first pair of twos and I’m going to say greatest common factor. We’re going to say 2 because we have 2’sM we have a pair of 2’s then I’m going to use this pair of 5’s here and I’m going to have 2 times 5. Now the extra 5 this 5 and this 2 do not get used because they don’t have a pair from the other number. If I had an extra let’s say I had an extra 2 up here then I could use this 2 from 20 and this 2 but because I don’t have that extra pair, I can’t use them. I can only use the numbers that have a pair from both. Now our greatest common factor is going to be 2 times 5 which is 10. The solution to the greatest common factor between 50 and 20 is the number 10. Let’s do a couple practice problems from our greatest common factor worksheet.

Number one on our gcf worksheets gives us the numbers 12 and 40 and asks us to find the highest common factor between them. What I’m going to do is I’m going to take the number 12 and the number 40 and I’m going to break them down using prime factorization. 12 is even so I’m going to use the number 2. I’m going to start with the number 2 and 2 times 6 is going to be 12. 2 is a prime number but 6 is not. Now I can break 6 down into 2 times 3 and then for 40. 40 is an even number. I’m going to use 2. 2 times 20 is 40. 20 again is an even number so I’m going to use 2 again, this would be 2 times 10. 10 is an even number and I’m going to say 2 and then 2 times 5 is 10. Now I have my prime factorization. All of these are prime so I know it’s been factored correctly. Now what I’m going to do is I’m going to list out my numbers 12 and 40 into prime factorization. 12 was 2 times 2 times 3 and 40 was 2 times 2 times 2 times 5. Then we can grab the pairs of numbers that are in both 12 and 40. If we look, we have a pair of twos the very first numbers or pair of two. We’re going to use those and then we also have a second pair of twos here. We’re going to use those and then we have for the number 12 we have a 3 but 40 does not have a 3. We can’t use this 3. 40 has another 2 but 12 does not have a 2 to go with it so we can’t use that 2 and then for the 5 and 40 we can’t use it because 12 does not have a 5. Our greatest common factor is going to be the pairs of numbers that we can multiply together. We have a two this prime factor of two times the other two the other prime factor of two. Our greatest common factor is going to be two times two which is four and four is going to be our greatest common factor between 12 and 40.

The next problem we’re going to show you on our greatest common factor worksheets for teaching you how to find the highest common factor is number four. This gives us 32 and 28 as the numbers that we need to find the greatest common factor of. The first thing I’m going to do is I’m going to factor this out using the prime factorization methods. 32 is an even number so I’m going to break it down into 2 times 16. 16 is an even number so I’m going to say 2 times 8. 8 is an even number so I’m going to say 2 times 4 and then 4 can be broken down into 2 times 2. 28 is also an even number so I’m going to say 2 times 14 and then 14 I’m going to say 2 times 7.  Now we have our numbers listed out in prime factors and I’m going to circle them here. I’m going to take 32 and I’m going to list it by its greatest common factors which are going to be in this case 32 is 2 times 2 times 2 times 2 times 2, five twos and then 28 when I list 28 out it’s going to be 2 times 2 times 7. To find the greatest common factor we’re going to take our list of prime factors that both numbers share. In other words you could say the pairs of prime factors. Our first pair is going to be this first two. We’re going to say two then our second pair we have another set of twos. Another pair of twos and then if we look 32 has a bunch of twos. Two, two, two, but 28 doesn’t have any more twos so we can’t use those twos. 28 has a seven. Seven is not in 32 so we can’t use that 7 either. Our greatest common factor is going to be 2 times 2 which means that the greatest common factor between 32 and 28 is 4. Hopefully you found this video helpful for teaching you how to find the gcf. Try all the practice problems by downloading the free greatest common factor worksheets above.