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.

I got this in the first 1:27 seconds, I was like "Ohhhhhhh."

isnt this basic math not pre algebra

do i all way's have to watch math vid's for my math class

u forgot multiples or LCM

GCM is greatest common mistake, I got this joke from my math teacher.

Why are people calling you stupid captain duckface? Just Shut Up All Yall!

Hey did you write Gcd

Thank u

what recording program do you use?

the reason 25 has an odd number of factors is cause its a square number.

i wonder what happens if videos are what teachers yuse these days ?

Here for my goddamn homework…

lol

Laggy

how about finding gcd using euclidean algorithim?

THX U SO MUCH

that rlly helped me

thank you khan academy

Thx even though this was uploaded the year I was born in XD

ASMR

Odd numbers have and odd amount of factors and even numbers have an even amount of factors. Right? Please answer me.

hi

тнє нєℓρє∂ мє ωιтн му 82 qυєѕтισи¢ρα¢кєт

You really help me! 😀

Thanks this helped a lot

You are awesome. You have helped me pass so many college courses!!!

it is great. thank u

yee

GCF means Greatest Common Factor and I'm listing with earbuds/earphones what ever you call them 🎧

thank you so much you are better than my teachers at my school and you always allow me to get high grades but i think that you should consider getting a new microphone so that we can hear you without the crackling sound

are GCF and HCF the same ??

Typically not typical as deductic logical.

To think this video has been uploaded back in 2006… I wonder when Sal actually founded Khan Academy.

you really hate the number 1 hahaha

First lol

My mom made me watch this video even though I know what a greatest common factor is, who owns this computer.

The worst

divisor makes sense than factor

SAL VOICE SOUNDS SO MUCH HIGHER

Thank u so much for this vid it helped me with my homework 😊😊😊😊

What the factors

I knew all of the factors part but the part I was struggling with was finding the GCF. Thank you so much! It helped me clear out my concern for it! 🙂

this sucks

thank you it helped me in school

lmAOO

because the rest are prime

Thx khan academy

I'm here because I have a test tomorrow 😭

Ella said your annoying

did it

1,000th to like XD

huh.. it was getting intresting

Helped me with my review homework, I had forgotten what it was, haha! Thanks so much.

this guy is so cunfusing

Any this for large numbers? (Anything above a hundred below I got)

Wtf of The date? I was of 7 months old men =/ now I have 11 years god

Thanks this really helped me in my work now I understand

6:14 and then he never does! LOL!!!!

Im still confused? can you explain a little more?

U sound depressed

What software (And hardware if you know) does he use to draw?

thanks teasher شكرا استا

Kill. Me

thank you so much you saved my life

I am not confused

4:21 lol, disappointed

this is a good video

Can a GCF be a decimal

what if the GCF was 19077

i wont keep counting all the multiples to 19077

Farah mama

this video was really helpful thanks!

also 200 comments

it's so interesting to see how your Sal's videos have improved over the years. I'm currently doing Khan Academy in Year 10, using it to relearn the fundamentals of maths rather than traverse this hodge podge curriculum we're given. I was doing the HCF area and I suddenly saw the quality change and I must say it's amazing how it's improved over the years

Threes days before my exam and this is the first time I’ve learned that the GCF means the largest of the common factors of the numbers. My math teacher failed to mention that. Thank you

how do you know what the greatest factor is????

Luv it thx!!

This video is a year older than me :O

Thanks khan academy is the best 😃😃😃

Thank you, I

don't know why my teacher didn't teach me this way.

what do you meeeeeeaaaan??!?!?!

just sad:(

He is so helpful

omg how that much subscribers?

I WAS BORN WHEN THIS VIDEO WAS MADE

What everyone at schools ays when they dont get it OOOOOOHHHHHHHHH

Thanks 🙂

This was really helpful

Back when 240p was high resolution.

doing khan academy and i get this video

this must be the oldest video in the channel. I think was two on the time of the release!

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

This video is 2 years older than me :/