Greatest common divisor

Well, when you look at it numerically you see that both 6 and 15 are divisible by 3.

And that's interesting.

But we saw before, we could put into reduced form.

You got it five.

I'll try to be more creative when I think of my numbers.

The mathematics community should settle on one of the two.

And in other videos I've explained why this works.

That's what v squared is, times v times v.

Euclid's algorithm is incredibly simple.

Well you can think of what's the biggest number that divides into both of these numbers?

When you look at the prime factorization, the only thing that's common right over here is a 3

So the best way to do that is just to figure out what is the

Let's do another problem.

Let's do another problem.

Taking a step back, this first one made sense.

Now, both of these numbers have a 2 times 2 in it, or they're both divisible by 4.

Well, these two both have a 3 and they both have a 5

Well, that's it for now.

So, our greatest common divisor of 10 and 7, so let me write that down, so we have 10

And the easiest way we can do that, is say hey, is there any common factor?

Eventually you're going to say, hey, wait, look, the

So 36 8 is the same thing as so we can simplify, dividing the numerator and denominator by 4.

So we think of what's the largest number that divides into all three of these?

So, 21 and 30 are the two numbers that we care about

If a b, we're going to return a.

We're going to reserve a proof for it for an algebra class that you might take in college or in high school.

Otherwise, else.

Another way to say this is, gcd(20, 40)  ?

So just to be clear, first of all, when someone asks you what's the greatest common divisor of twelve and eight?

Or you can break it down into its core constituencies, its prime factors, and then figure out what is the largest set of common prime factors

Least common multiple

So with that out of the way, let's figure out, what is the greatest common divisor or the greatest common factor of twelve and eight?

We're asked, What is the greatest common divisor of 10 and 7? Let's now break out our paper for this

Let's do one more

And notice, I can't reduce this anymore.

The easiest way or the fastest way is to say, hey, 16 is the biggest number that goes into both of these.

And if we look at all of these numbers, they all look divisible by 5.

And if we want to put this in simplest form, we just have to think about what is the largest number that divides into both 15 and 25?

Or you can think of it as what is their greatest common divisor?

And now, what are the common factors? Well, 1 is a common factor. 3 is also a common factor

People must have put in math terms and suddenly they find yeah there is this compilation

Max number

So let's divide the numerator and the denominator by 2, because they are both divisible by 2.

And 25 divided by 5 is equal to 5, and now we have 3 5.