Name: Greatest common factor explained | Factors and multiples | Pre-Algebra | Khan Academy
Uploaded: 2016-12-23T17:01:07.000Z
Duration: 6 min 20 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

The superlative

Welcome to the greatest common divisor or greatest

To-infinitive

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

I mean, really a divisor is just a number that can divide

into something, and a factor-- well, I think, that's also a

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

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.

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.

Pretty much every whole number or every integer has

They both share the common factor 2 and they both

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.

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.

What is the greatest common divisor of 25 and 20?

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

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.

So the greatest common divisor or greatest common factor of 25

What is the greatest common factor of 5 and 12?

It has no factors other than 1 and itself.

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

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.

Let's do the greatest common divisor of 6 and 12.

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Greatest common factor explained | Factors and multiples | Pre-Algebra | Khan Academy

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