what is the GCF of 8 and 20

okay my turn

GCF of 8 and 12

look at the little one 8

factors of 8 are 1,2,4,8

Now look at these factors - biggest to smallest.

Does 8 go into 12 NO

Does 4 go int 12 YES   so 4 is the GCF

The GCF is  $${\mathtt{4}}$$ . Do you want the explanation?

YES DRAGON THIS QUESTIONER NEEDS AN EXPLANATION!

Here's a rather odd method of determining this....but it works!!! It's called the  "Sieve of Eratosthenes"

First take the smaller given number and subtract it from the larger......so we have......

20 - 8   = 12   ........Now, does 12 divide both 8 and 20???  Nope.  Now, compare what we subtracted (12) and the result we obtained (8) and, again, subtract the smaller from the larger.

So we have    12 - 8   = 4........Now, does 4 divide 8 and 12?? Yep. And that's our GCF...!!!

Why does this work?? Because if a number divides two subtracted quantities, it also divides their sum. So 4 divides 8 and it also divides 8 + 12 = 20 !!!

Note, if we use this process on two numbers and we end up with a  "1," the numbers are relatively prime to each other. That makes sense......only one non-zero number divides two relatively prime numers....namely, 1 !!