We want to determine the factors of ninety-six.
And factors are whole numbers that divide evenly into another whole number.
So we want all the whole numbers that divide evenly into ninety-six.
It's also true that if x times y equals ninety six,
and x and y are whole numbers, then x and y would be factors of ninety-six.
So to find all the factors of ninety-six,
we're actually going to use this definition of a factor.
But to help us do this, we're going to use the prime factorization ninety-six
to make sure we get all of the factors at ninety-six.
So we'll start making a prime factorization tree for ninety-six.
Well ninety-six is even, so we could break this down into two times forty-eight,
where two is prime.
We can break down forty-eight into four times
twelve. Four breaks down into two times two,
which are both prime. Twelve breaks down into
three times four, where three is prime and then four is two times two.
So the prime factorization of ninety-six
would be one, two, three, four, five factors of two,
and one factor of three.
And now we're going to use this
to help us determine pairs of whole numbers
that have a productive of ninety-six. Well the two most obvious factors of ninety-six
would be one times ninety-six, which are both factors of ninety-six.
Then looking at the prime factorization of ninety-six,
we could write ninety-six as two times all of these factors.
Well that would be forty-eight, so we can write ninety-six is two times forty-eight,
which will give us two more factors of ninety-six.
We could also write ninety-six as three
times these five factors of two,
that's going to be three times thirty-two.
So there's two more factors of ninety-six.
Four is also a factor of ninety-six as
we see here. So we can write ninety-six as four times,
this here would be, eight times three, or twenty-four, so four times twenty-four
equals ninety-six.
We can see five is not a factor of ninety-six, but six is.
Here we have six and this would be
four factors of two, which is sixteen. So six -times sixteen is equal to ninety-six,
so there's two more factors.
Sevens not a factor of ninety-six, but eight is.
Here's a factor of eight, so we'd have eight times
two times two, times three, or eight times twelve.
And again looking at the prime factorization, we can see that nine is
not a factor of ninety-six, ten is not, eleven is not, ad twelve is.
And notice how we already have a factor of twelve here.
So now we've found all of the factors in ninety-six,
let's go ahead and list them. So the factors of ninety-six
will be one, two, three, four,
six, eight, twelve, sixteen, twenty-four,
thirty-two, forty-eight and ninety-six.
And we should list them in order from least to greatest, as I've done here.
So as you can see it was a little extra work to determine the prime factorization of ninety-six,
but it was helpful to make sure that we found all of the factors of ninety-six.
We'll take a look at one more example in the next video.