hey everyone it's kaylee thanks for joining me in the third video on greatest common factors in this
video we're going to use the prime factorization method to find the gcf of three numbers let's go
joe has four sandwiches six glasses of milk and eight cookies and wants to know how many identical
lunches he can make with no leftovers so really what is this asking us yeah it's just asking what
is the greatest common factor of 4 6 and 8. so if we do a quick prime factorization of 4 we get
2 and 2 and that's it right so 4 is just equal to 2 times 2. now if we do that for 6 we have
6 gives us 2 and 3 and that's it right 6 is equal to 2 times 3. now what about 4 8
8 gives us 2 and 4 and here we get another branch 4 is 2 and 2 so for 8 we can say
2 times 2 times 2. so what's my next step here yep finding those common factors
but it looks like i have a 2 here a 2 here and a 2 here and then i have matching factors
between this 2 and my 8 and this 2 here my 4 but there's nothing matching here in my 6
so that doesn't count and that doesn't count so that means i really only have
my gcf of four six and eight has just one factor
two so whenever i have just one matching factor between all of these then just that matching
factor becomes our greatest common factor and we can think about this as being two times one
because each of these twos would also have a little one a two and a one coming off of them
so greatest common factor is equal to two so that means joe can make two identical lunches
with no leftovers so what would joe's identical lunches look like well if we divide the sandwiches
into two each lunch would have two sandwiches and what about the milks each lunch would have
three milks and finally for the cookies each lunch would get four cookies those are some pretty
big lunches so here's another practice problem it says what is the greatest common factor of 36
27 and 18. so even though i have three numbers here what's my first step yeah we need to do
prime factorization of all three of these numbers so let's go ahead and start with 36.
i know 2 goes into 36 how many times 18 times and 18 breaks in two 2 and a 9 and 9 breaks into
3 and 3 so i can say 36 if i list out the factors is 2 times 2 times 3 times 3.
okay let's do the same thing now for 27. so 27 i get branches what's my first prime
number is three and a nine nine gives me three and three and that's it so 27 is equal to three
times three times three awesome last one let's do it for 18. i can divide by two and that gives me
nine and nine is three and three so 18 is equal to 2 times 3 times 3. okay so now what do i do
i need to find matching factors and matching factors between what yeah all three of these
numbers 36 27 and 18. well right off the bat here i see 27 only has threes in it right so
that means this 2 and 18 isn't matching with 27 and these twos don't match with 27 either
so they're out of the picture so in 36 i have two threes here and 18 i also have two threes so in 27
i can only take two of my threes that are matching and then what do i do with my matching factors
yeah i multiply them together so this will tell me that my greatest common factor my gcf of 36 27
and 18 is going to be equal to the product of our matching factors between
all three numbers which is two threes so three times three which i'm sure you know
is nine so the greatest common factor of 36 27 and 18 is nine did you notice that finding the
gcf of three numbers is pretty much the same as finding the gcf of two numbers
we just have to find the matching prime factors in our prime factorized asynchrony
and multiply them together now we can move on to our last gcf video and do some examples together