hey everyone it's kaylee this is the second video on greatest common factor we're going to
learn a new method for finding the greatest common factor of two numbers by using prime factorization
make sure you already know how to do prime factorization before we start this video let's go
just like finding our lcm we can write the question as gcf of 24 and 32.
now this is asking us what is the greatest common factor of 24 and 32 but instead of listing out all
the factors for 24 and 32 we can start with prime factorization trees so let's make our tree for 24.
so our tree for 24 starts with a 2 and a 12 and 12 turns into 2 and 6 and 6 turns into 2 and 3.
so i can write 24 is equal to 2 times 2 times 2 times 3 awesome let's do the same thing now for 32
so we have 32 starts with 2 and 16 16 gives us 2 and eight eight gives us two and four and
four gives us two and two so i can also write 32 here is equal to two times two times two times 2
times 2 okay so now we're going to take a look at these lists our factors here for 24 and 32 and
we're going to find all of the matching factors so i have a 2 right here and i have a 2 right here
and i have a 2 here and a 2 there and a 2 here and a 2 here and then i have a 3 which is not here
and these extra 2s i don't have over here so my matching factors are these three twos so i can say
my greatest common factor of 24 and 32 is going to be the product so multiplication
of my matching factors here which is 2 times 2 times 2. now why does this work
well i know that this 2 here is divisible into 32 and 24 because they both have it in their list
and i know that this next two here also goes into 24 and 32 and i know the product as well
because i have it here with a multiplication sign in here with the multiplication sign
and i know that this last two is also divisible into 24 and 32 by the same logic
it's here in my list of factors and it's able to be multiplied by the other two factors so while
i know that this 1 2 is divisible in the 24 and 32 these three twos are also divisible into 24 and 32
and are the greatest number that's divisible in 24 and 32. so if i do my multiplication
here 2 times 2 is 4 times 2 is equal to 8. so 8 is the greatest common factor of 24 and 32.
this one says find the greatest common factor of 88 and 68. so we could solve this one by
listing out each factor for 88 and 68 and then find the largest matching factor between them
let's start by listing the factors of eighty-eight so of course we have one times eighty-eight
and we have two times forty-four and what else uh not three but four four
times twenty-two okay are there any more does five go into eighty-eight no does six no
nine no eight eight does right eight times eleven okay so what about nine no 10 no
okay i'm gonna call this list good for now for 88 and now let's come over here and do the same thing
for 68. or can you think of another method that doesn't involve a bunch of division yeah prime
factorization so let's make our prime factor tree for 88. so we know 2 goes in there 44 times and 2
goes into 44 22 times and 2 goes into 22 11 times and that's all we got because 11 is a prime number
so we can say 88 is equal to 2 times 2 times 2 times 11. okay now we can do the same thing for 68
68 our tree here we have 2 and 34 and 34 we have 2 and 17 and that's it because 17
is also a prime number so for 68 we have 2 times 2 times 17. so what's my next step
yep i got to find my matching factors here so it looks like this one i got a 2 right here
and i got a two right here and here is another two which matches here and then i have a two here
but no more twos i just got my prime 17 and my 11 so it looks like i only have two matching factors
so i know i take the product of those two so my greatest common factor of 88 and 68 is going to
be equal to 2 times 2 is equal to 4. wow so much easier than doing all of that arithmetic
so now we know the faster way to find the greatest common factor is using
prime factorization and finding those matching factors let's watch the next
video to learn how to find the greatest common factor of three numbers see you there