so we want to fill this area with square tiles and so it has to fit perfectly so we have a lot of possibilities let's take each dimension separately so for this length here is 72 to make that 72 inches and ignoring that 42 for a second you could have tiles that are a certain size and a certain number so you could try to make one big one let's do number size so you could try to do just one big 72 inch tile to try to fill the space but clearly that's not going to work at this side here is only going to be 42 so we could also do two tiles each of size of 36 but the 36 isn't going to work on that side so let's keep just kind of going with this we could do three that would each be M mu 2 divided by 3 is 24 and we could do 4 and that's 18 I swear the arithmetic is the hardest part I couldn't do 5 inch tiles because 5 inch tiles wouldn't fit right along that 72 but you could do 6 and 12 I can't do 7 but you could do 8 and 9 and once you see that 8 and 9 your next number that you would be checking be 9 and that starts to repeat so you can just work your way back the other way you could do 9 8 12 6 inch tiles 18 orange tiles 24 3 inch tiles 36 2 inch tiles and 72 1 inch tiles just for completeness of the table so this is in the number of ways you could possibly make this dimension happen but remember you also have to take care of that dimension 42 and so the number of tiles you could have you could have one big 42 inch tile or you could have two 21 inch tiles running the side or three and 14 for does not work five does not work six and seven and then again when you get the seven you can start to repeat routine 321 240 to 1 so now these tiles have to pay the same size in both directions clearly so we need to find the ones that they have in common and what you're going to write when you're writing out your answer for this is that we're finding common factors of 72 and 42 so let's see they both have to go by the size so he can't make a 72 he can't make a 36 he can't make a 24 he can't make it 18 he can't make it 12 nor 9 Wow nor an 8 ah there we go finally they can both have 6 inch tiles that will work for both of them no 4 but a 3 will work a to work and a 1 it will work so when they say find different three different size tiles that will work to fill the space we've actually found 4 so we could use 6 inch tiles 3 inch x 2 inch tiles or 1 inch tiles and these are our common factors now the next thing they ask is what if we want to use the least amount of tiles possible to fill the space well if we want to use the least amount possible we want to use the biggest tile so in this case we want to use 6 and that biggest one is the greatest common factor right the greatest common factor is 6 so we're going to want to use a 6 inch tiles to fill the space and we're not quite done yet because they ask well how many tiles would you use so if we use 6 inch tiles we would need a 72 divided by six we would need whoa brain freeze 12 we would need 12 tiles going across this way and 42 divided by six we need seven tiles going up that way to make a total number of tiles of 12 times 7 is 84 tiles and that's the least amount of tiles you can use to build the space that's that

thank you so much for these videos!!

This was simple and great!! Thank you!

Your videos have been a big help!

I love the way you teach math so simply..it helps me to get it. Pls never delete your videos, I value them! Thank you so much Laura R.

Thank you so much! This was one that I was struggling so much with and you answered in a way that will allow me to totally ace it. Thanks!