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Greatest Common Factors - Problem 1
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One of the skills you might have already learnt is how to find the greatest common factor of two numbers. If you haven’t learnt it yet I’m going to show you now.

I’ve been asked to find the greatest common factor of 24 and 60. So what I’m going to do for each of those numbers is go through and list all the factors I can think of and then find the biggest one that shows up in both lists.

So for 24 I’m going to start like this. I know that 1 times 24 gives me the answer 24. I’m going to go in pairs. 2 times 12 gives me the answer 24. 3 times 8 gives me the answer 24 and also 4 times 6. And then I know I’m done because I checked 1, 2, 3, 4, 5 doesn’t go into 24 and then I’m already at 6 which will match with 4. These are my factoring pairs.

Lets do 60, same process. I’m going to start with 1 and 60 because I know 1 times 60 is 60. Then I’ll have 2 and 30, 3 and 20. Does 4 go into 60? Yeah, 4 times 15. 5 goes into 60 12 times. So I have 5 and 12. 6 goes into 60 ten 6 with 10. 7 does not go into 60, 8 does not go into 60, 9 does not go into 60 and then I’m already at 10. That way I know I’ve checked all of my factors.

So what I’ve done so far is just list all the factors and I need the greatest common factor. That means the biggest number that shows up n both lists. So let’s see. I’m going to start with my biggest ones here, see if they show up there. 24 is not in there, oh good, 12 is. There we go, that’s my answer. The greatest common factor of 24 and 60 is 12. That’s the biggest number that multiplies into both of them.

I’m going to use the same process here with 18x squared and 27x to the 3rd. for 18 and 27 I want to think of the biggest number that multiplies into both of them. After a while you can start to do this in your head a little bit without writing out this whole long list. Like things that go into 18 are like 1 and 18 but 18 doesn’t go into 27. 2 and 9 and good, 9 does go into 27. So what I’ve kind of done is this process in my head. I know the greatest constant or the greatest number that goes into both of those is 9.

Now I’m going to think about the Xs. How many Xs go into both x squared and x to the third? And the answer for that one is x squared. That’s my greatest common factor. When you’re doing these problems, if you want to and probably it’s a good idea in the beginning, write out that whole big long list. Once you get better at that and you start recognizing patterns you can start doing it in your head and looking for the number that goes into both of these numbers or coefficients and then also think about how many Xs or variables go into both of your variable terms. That’s how you guys can find the greatest common factor either if you have two numbers or two constants that are attached to variable quantities.

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