### Video Transcript

Find the GCF of 56ππ and 46π, given that π and π are positive, whole numbers.

GCF stands for greatest common factor. So what we need to do is to take 56ππ and 46π and separate it into its prime factors. Letβs begin with 56ππ. 56 is eight times seven. Seven is a prime number. So we can leave it alone. But what does prime mean?

To be prime means that it will have exactly two factors, one and itself. So here, seven can only be broken down into one times seven, one and itself. However, eight is four times two, where two is prime. So we can leave that alone. But four is two times two. So weβve broken 56 down to its prime factors. π is simply π and π is simply π.

Now, if they had been something like π squared π, we could see that π squared could be broken down into π times π. But we donβt have that. So 56ππ could be rewritten as two times two times two times seven times π times π. And if we wanted to, we could rewrite two times two times two as two cubed.

Now, letβs take a look at 46π. 46 is two times 23, where two is prime and 23 is prime. And then, π is all by itself. So we can rewrite 46π as two times 23 times π. So now, weβre asked to find the greatest common factor. So what is the factor thatβs the greatest that they have in common? Well, comparing these two numbers, they each have a two and a π. Therefore, the greatest common factor between these two numbers would be two π.

Now, if, for example, we had the same problem but we have this extra two over here, then they would have these twos in common and these twos in common. So you would take two times the other set of twos that they have in common and multiply them together to be four. And then, they each would have a π. So the greatest common factor would be four π.

However, in our case, our final answer will be two π.