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Greatest common factor explained

CCSS.Math:

Video transcript

welcome to the greatest common devisor or greatest common factor video so just to be clear first of all when someone asks you whether what's the greatest common divisor of 12 and 8 or they asked you what's the greatest common factor of 12 and 8 that's that's a C back there for common I don't know I came in like that they're asking you the same thing I mean really a divisor is just a number that can divide into something and a factor well I think you that that's also a number that can divide into something so a divisor and a factor are kind of the same thing so with that out of the way let's let's figure out what is the greatest common divisor or the greatest common factor of 12 and 8 well what we do is it's pretty straightforward 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 does not go into 12 6 goes into 12 because 2 times 6 and then 1 goes into and then 12 goes into 12 of course 1 times 12 so that's the factors of 12 let's write the factors of 8 well 1 goes into 8 2 goes into 8 3 does not go into 8 4 does going to 8 and then the last factor pairing up with the 1 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 & 4 and what's the greatest of them well well that's pretty easy it's 4 so the greatest common factor of 12 and 8 is 4 let me write that down just for emphasis greatest common factor of 12 and eight equals four and of course we could have just as easily had said the greatest common divisor of two of twelve and eight equals four sometimes it does thinks it will find Grace contraction 24 let's do another problem what is the greatest common divisor of 25 and 20 well let's do it the same way the factors of 25 well it's one the two doesn't go into it three doesn't matter 4 doesn't go into five does it's actually 5 times 5 and then 25 it's interesting that this only has 3 factors I was I'll leave you to think about why this number only has three factors and other numbers and tend to have an even number of factors and then now we do the factors of 20 the factors of 20 or 1 2 4 5 10 and 20 and if we just look at this by inspection we 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 greatest common factor of 25 and 20 well that equals 5 let's do another problem what is the greatest common factor of 5 and 12 well factors of 5 pretty easy one in five and that's cuz it's a prime number it has no factors other than 1 and itself and then the factors of 12 12 is a lot of factors it's 1 2 3 4 6 and 12 so it really looks like the only common factor they share is is 1 so that was I guess in some ways kind of disappointing so the greatest common factor of 5 and twelve is one and I'll throw you out so I'll throw out some terminology here for you when two numbers have a greatest common factor of only one they're called relatively prime and that's that's that kind of makes 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 one as their greatest common factor hope I didn't confuse you let's do another problem let's do the greatest common divisor of 6 and 12 out of 12 coming up a lot I'll try to think of be more creative when I think of my numbers well the greatest common divisor of 6 and 12 lists the factors of 6 are 1 2 3 & 6 factors of 12 1 2 3 and we'll 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 apologize 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 equals 6 so it actually equals 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 in the near future that it'll give you more example problems