Greatest common divisor

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

And notice, I can't reduce this anymore.

And that's interesting.

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

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.

You got it five.

Taking a step back, this first one made sense.

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.

We can simplify this further twelve and forty five have common factors.

And then 100 divided by 4 is 25.

Well the largest number that divides into all of these guys is twenty.

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 this is going to be the same thing and I think the least common multiple of nine and five is going to be forty five.

For example, if we want to find the phi of 8, we look at all values from 1 to 8, and then we count how many integers 8 does not share a factor greater than 1 with.

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

The will is there.

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

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.

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

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)  ?

Well, he is now, that's for sure.

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

Least common multiple

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

So we could say that this is the same thing as 36 hundredths or this is equal to 36 over 100.

You should do something as a representative Should do that? The wig thing?

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

The straight line of points along the top represents all the prime numbers.

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