Here I show you how to use Prime factorization with factor trees to find the GCF of two larger numbers. Greatest Common Factor is the largest possible number that can divide two other numbers evenly.
Transcript
0:00 Hey everyone! This video is going to show you how to find the GCF or the greatest common factor. I have another video that talks about prime factorization which we’re going to use in this video, so if you don’t know what prime factorization or factor trees are, then you should watch that. I’ll put a link for you down in the comments below.
0:21 This is really helpful when you are trying to find the smallest number possible that will go into two different numbers, because a factor is just that – it’s a number that you can use to multiply by to get this larger number.
0:45 I’m going to start with the same numbers that I used in my other videos. We’re going to find the greatest common factor for 250 and 360.
1:01 The first step that I need to do is find the prime factors for each of these numbers. I’m going to use a factor tree in order to do that. For 250, I’m going to factor that into 25 * 10, and then each of those numbers can be factored into 5 * 5, which are both prime, and then 2 * 5, which are both prime. So I’m done with that one. I have all of my prime numbers that make up 250.
1:32 For 360, I’m going to do the same thing. 360 is 36 * 10, and then this is 6 * 6, and this is 2 * 5, which both of those are prime, so I’m done there with that number. But my sixes can be factored into 2 * 3, 2 * 3. So I have all of my prime numbers listed for each of my larger numbers.
2:05 Let me show you what to do with those. It makes it really easy if you list out each of these numbers from smallest to largest.
2:19 There we go. I turned on the light for you because it seemed like it kept getting blurry.
2:23 So again, my factors are 2 * 5 * 5 * 5, and then my factors for 360 are 2 * 2 * 2 * 3 * 3 * 5.
2:46 I’m listing them out here nice and neat because now what I need to do is find my common factors. In other words, what numbers are the same in both of these prime factorizations for both of these numbers?
3:00 Well, I see that they share a two, so I’m going to write a two down here. This number 250 doesn’t have any more twos, so I can’t use these, and it doesn’t have any threes either, so I can’t use those. But it does have a five in common, and I’m not going to use these other fives because there’s no other five down here that can match up with these fives.
3:32 So I have my 2 * 5, which is 10. So that’s my GCF!
3:37 There you go. I hope that was easy enough for you. If you have any questions, please let me know and check out my other videos, especially my factor tree video. And if you’re also needing to figure out LCM (lowest common multiple), I have a video on that as well.
3:52 Thanks!
Extra Credit
I also have a few awesome math resources for you! Check out all of my Spiral Review Digital Task Cards listed here:
- 2nd Grade Spiral Review – https://bit.ly/3mFEJLA
- 3rd Grade Spiral Review – https://bit.ly/3kJatxp
- 4th Grade Spiral Review – https://bit.ly/2ZYYl3A
- 5th Grade Spiral Review – https://bit.ly/32SOeiJ
- 6th Grade Spiral Review – https://bit.ly/3mKW7hW
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