Welcome to the greatest

common divisor 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 ask you what’s

the greatest common factor of 12 and 8? That’s a c right

there for common. I don’t know why it

came out 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, 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 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 of 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 to go into 12. 6 goes into 12

because 2 times 6. 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 go into 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 the 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 4. Let me write that down

just for emphasis. Greatest common factor

of 12 and 8 equals 4. And of course, we could have

just as easily had said, the greatest common divisor

of 12 and 8 equals 4. Sometimes it does

things a little funny. 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 1. 2 doesn’t go into it. 3 doesn’t go into it. 4 doesn’t go into it. 5 does. It’s actually 5 times 5. And then 25. It’s interesting that

this only has 3 factors. I’ll leave you to think about

why this number only has 3 factors and other numbers

tend to have an even number of factors. And then now we do

the factors of 20. Factors of 20 are 1,

2, 4, 5, 10, and 20. And if we just look at this by

inspection we see, well, they both share 1, 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. 1 and 5. That’s because it’s

a prime number. It has no factors other

than 1 and itself. Then the factors of 12? 12 has a lot of factors. It’s 1, 2, 3, 4, 6, and 12. So it really looks like 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 out some

terminology here for you. When two numbers have a

greatest common factor of only 1, they’re called

relatively prime. And that kind of makes sense

because a prime number is something that only has 1

and itself as a factor. And two relatively prime

numbers are numbers that only have 1 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. I know 12’s coming up a lot. I’ll try to be more creative

when I think of my numbers. Well, the greatest common

divisor of 6 and 12? Well, it’s the factors of 6. Are 1, 2, 3, and 6. Factors of 12: 1, 2, 3–

we 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 apologize that I keep switching

between divisor and factor. 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’ll give you more

example problems.

this video belongs in a museum

Ahhhhhhhhhhhhhhhhhh my eyes!!!!!!!!!!!!

this guy i understand this problem nice

you made it simple for me.. thank you

is greatest common factor has the same meaning of highest common factor if someone knows please replayyyyyyyyyy impp

Is this cheating for my piece of my lord homework

Oh woooow I was born when this video was made lol 😂😂😂😂😁❤️😂😂😂😁😁

nice helping me with my math

thx khan academy

Fun fact:This video was recorded on a potato

Khan academy is the best