Learn about the Greatest Common Divisor Video

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Learn about the Greatest Common Divisor

Learn about the Greatest Common Divisor Welcome to greatest common divisor or greatest common factor video. So just to be clear, first of all, when someone ask you whether what’s the greatest common divisor of 12 and 8 or they ask you what’s the greatest common factor of 12 and 8 that’s a c right there for common I don’t know like you know that. They’re asking you the same thing, I mean really a divisor is just a number they can divide into something and a factor well I think you—that’s also a number they can divide to something . So a divisor and a factor are kind of the same thing. So that other way let’s figure out what’s the greatest common divisor or the greatest common factor of 12 and 8. Well, what we do is--it’s pretty straight forward. First, we just figure out the factors of each of the numbers, so first, let’s write all the factors out of the number 12. Well, 1 is a factor, 2 goes into 12, 3 goes into 12, 4 goes into 12, 5 doesn’t go into 12, 6 goes into 12 that’s 2 times 6 and then 12 goes to 12 of course 1 times 12 so that’s the factors of 12. Let’s write the factors of 8. 1 goes into 8, 2 goes into 8, 3 doesn’t go into 8, 4 does go into 8 and then the last factor pairing up with the one is 8. So now, we’ve written all the factors of 12 and 8 so let’s figure out what the common factors of 12 and 8 are. Well, they both have the common factor of 1 and that’s really not so special pretty much every whole number or every integer has a common factor of 1. They both share the common factor 2 and they both share the common factor 4. So we’re not just interested in finding a common factor, we’re interested in finding the greatest common factor. So all the common factors are 1, 2 and 4 and what’s the greatest of them? Well, that’s pretty easy it’s 4. So the greatest common factor of 12 and 8 is four, we write that down just for an emphasis, greatest common factor of 12 and 8 equals 4 and of course we could have just as easily it set the greatest common divisor of 12 and 8 equals 4—sometimes it does takes―. Let’s do another problem. What is the greatest common divisor of 25 and 20? Well, let’s do the same way. The factors of 25 well it’s 1, 2 doesn’t go, 3 doesn’t go,4 doesn’t go into it, 5 does, it’s like your 5 times 5 and then 25. That’s interesting that this only have three factors. Now, I’ll leave you to think about why this number only has three factors and another numbers tend to have an even number of factors. And then now we do the factors of 20. The factors are 1, 2, 4, 5, 10 and 20 and if we just look at this pie and inspection we’ll see, well, they both share one but that’s nothing special but they both have the common factor of—you got it 5. So the greatest common divisor or the greatest common factor of 25 and 20 that equals 5. Let’s do another problem. What is the greatest common factor of 5 and 12? Well factors of 5, pretty easy 1 and 5 and that is a prime number has no factors other than 1 and itself. And the factors of 12, 0405 there are a lot of factors. It’s 1, 2, 3, 4, 6 and 12. So really it looks like the only common factor they share is 1 so that was—I guess in some ways kind of disappointing so the greatest common factor of 5 and 12 is 1. And I’ll throw you out some terminology here for you when two numbers have a greatest common factor of only one, they’re called relatively prime and that kind of make sense because a prime number is something that only has one and itself as a factor. And two relatively prime numbers are numbers that only have 1 as their greatest common factor. I hope I didn’t confuse you. Let’s do another problem. Let’s do the greatest common divisor of 6 and 12 and the 12’s coming up a lot, I’ll try to go be more creative when I think of my numbers. Well, the greatest common divisor of 6 and 12. What are the factors of 6 are 1, 2, 3, and 6. Factors of 12, 1, 2, 3, you should have these memorized by now 3, 4, 6 and 12. Well, it turns out 1 is a common factor of both, 2 is also a common factor of both, 3 is a common factor of both, and 6 is a common factor of both and of course what’s the greatest common factor—well, it’s 6 and that’s interesting. So in this situation, the greatest common divisor and I apologized that I keep switching between divisor and factor. They should—the mathematics community should settle on one of the two. The greatest common divisor of 6 and 12 is equal 6 so that should equal one of the numbers. And that makes a lot of sense because 6 actually is divisible into 12. Well, that’s it for now; hopefully you’re ready to do the greatest common divisor or factor problems. I think I might make another module the near future that will give you more example problems.

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Learn about the Greatest Common Divisor

Welcome to greatest common divisor or greatest common factor video. So just to be clear, first of all, when someone ask you whether what’s the greatest common divisor of 12 and 8 or they ask you what’s the greatest common factor of 12 and 8 that’s a c right there for common I don’t know like you know that.

They’re asking you the same thing, I mean really a divisor is just a number they can divide into something and a factor well I think you—that’s also a number they can divide to something . So a divisor and a factor are kind of the same thing. So that other way let’s figure out what’s the greatest common divisor or the greatest common factor of 12 and 8.

Well, what we do is--it’s pretty straight forward. First, we just figure out the factors of each of the numbers, so first, let’s write all the factors out of the number 12. Well, 1 is a factor, 2 goes into 12, 3 goes into 12, 4 goes into 12, 5 doesn’t go into 12, 6 goes into 12 that’s 2 times 6 and then 12 goes to 12 of course 1 times 12 so that’s the factors of 12.

Let’s write the factors of 8. 1 goes into 8, 2 goes into 8, 3 doesn’t go into 8, 4 does go into 8 and then the last factor pairing up with the one is 8. So now, we’ve written all the factors of 12 and 8 so let’s figure out what the common factors of 12 and 8 are. Well, they both have the common factor of 1 and that’s really not so special pretty much every whole number or every integer has a common factor of 1. They both share the common factor 2 and they both share the common factor 4.

So we’re not just interested in finding a common factor, we’re interested in finding the greatest common factor. So all the common factors are 1, 2 and 4 and what’s the greatest of them? Well, that’s pretty easy it’s 4. So the greatest common factor of 12 and 8 is four, we write that down just for an emphasis, greatest common factor of 12 and 8 equals 4 and of course we could have just as easily it set the greatest common divisor of 12 and 8 equals 4—sometimes it does takes―. Let’s do another problem.

What is the greatest common divisor of 25 and 20? Well, let’s do the same way. The factors of 25 well it’s 1, 2 doesn’t go, 3 doesn’t go,4 doesn’t go into it, 5 does, it’s like your 5 times 5 and then 25. That’s interesting that this only have three factors. Now, I’ll leave you to think about why this number only has three factors and another numbers tend to have an even number of factors. And then now we do the factors of 20.

The factors are 1, 2, 4, 5, 10 and 20 and if we just look at this pie and inspection we’ll see, well, they both share one but that’s nothing special but they both have the common factor of—you got it 5. So the greatest common divisor or the greatest common factor of 25 and 20 that equals 5. Let’s do another problem.

What is the greatest common factor of 5 and 12? Well factors of 5, pretty easy 1 and 5 and that is a prime number has no factors other than 1 and itself. And the factors of 12, 0405 there are a lot of factors. It’s 1, 2, 3, 4, 6 and 12. So really it looks like the only common factor they share is 1 so that was—I guess in some ways kind of disappointing so the greatest common factor of 5 and 12 is 1. And I’ll throw you out some terminology here for you when two numbers have a greatest common factor of only one, they’re called relatively prime and that kind of make sense because a prime number is something that only has one and itself as a factor. And two relatively prime numbers are numbers that only have 1 as their greatest common factor. I hope I didn’t confuse you. Let’s do another problem.

Let’s do the greatest common divisor of 6 and 12 and the 12’s coming up a lot, I’ll try to go be more creative when I think of my numbers. Well, the greatest common divisor of 6 and 12. What are the factors of 6 are 1, 2, 3, and 6. Factors of 12, 1, 2, 3, you should have these memorized by now 3, 4, 6 and 12. Well, it turns out 1 is a common factor of both, 2 is also a common factor of both, 3 is a common factor of both, and 6 is a common factor of both and of course what’s the greatest common factor—well, it’s 6 and that’s interesting.

So in this situation, the greatest common divisor and I apologized that I keep switching between divisor and factor. They should—the mathematics community should settle on one of the two. The greatest common divisor of 6 and 12 is equal 6 so that should equal one of the numbers. And that makes a lot of sense because 6 actually is divisible into 12.

Well, that’s it for now; hopefully you’re ready to do the greatest common divisor or factor problems. I think I might make another module the near future that will give you more example problems.

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