### Video Transcript

Let’s look at finding the prime
factorization of a number. Before we get started, there are
two words we need to know here. And that would be “factor” and
“prime number.”

Factors are numbers we multiply
together to produce another number. Here’s an example. Two times three is six. Two and three are factors of
six. And prime number is a whole number
greater than one that has exactly two factors: one and itself. For example, the number seven, the
only two numbers that multiply together to equal seven are one and seven. So seven is a prime number. Then, we say that prime
factorization is writing a composite number as the product of only prime
numbers. Just a reminder, a composite number
is a whole number greater than one that has more than two factors. For example, 10, you can find 10 by
multiplying one by 10 or two by five. 10 has more than two factors.

Okay, back to prime
factorization. We’re going to take these composite
numbers and write them as a product of prime numbers. Remember that product means numbers
that are multiplied together. We’re gonna look at two methods for
finding prime factorization: the first one is by using a factor tree and the second
one is dividing by prime numbers.

Find the prime factorization of
60.

Let’s start by using the factor
tree method to factor 60. What you wanna do here is think
of two numbers that you know that multiply together to equal 60. I’m gonna choose six and
10. Six times 10 equals 60. Now, we look at the numbers six
and 10 and we see what multiplies together to equal each of those. For six, I know that two times
three equals six. And for 10, two times five
equals 10.

The factor tree method is
finished when each of your branches is a prime number. So here, the only things that
multiply together to equal two are two and one. Two is a prime number. Three is a prime number for the
same reason: one times three is three. That’s the only factors. When we find that all of our
branches have prime numbers, we can stop and write down the prime
factorization. Two times two times three times
five is the prime factorization of 60. 60 equals two times two times
three times five. It’s often helpful to write it
with exponents. So we say two squared times
three times five for clarity. And we call this method the
factor tree method. Let’s solve the same problem
again using divide by prime numbers method.

For this method, I need to
think of a prime number that 60 is divisible by. I’m going to start with
two. I know that 60 is divisible by
two. And I know that two is a prime
number. 60 divided by two is 30. Now, I need a prime number here
that 30 is divisible by. I chose three. 30 divided by three is 10. We need a prime number that 10
is divisible by. I’m gonna choose two. 10 divided by two is five. This method is finished when
the number in the box is a prime number. Since five is a prime number,
we’re finished with this step. We take all the prime numbers
we’ve been using to divide and the bottom number. And this is the prime
factorization.

You would say 60 equals two
times three times two times five. Or more simply, two squared
times three times five. Both methods lead us to the
prime factorization of sixty. Though the methods are
different, there is only one prime factorization of 60. Only one set of prime numbers
multiply together to equal 60.

Our next example says, “Find
all the prime factors of 28.”

This time we’re gonna try and
divide by prime factors to solve the problem. I noticed that 28 is an even
number. So I’m gonna start by dividing
it by two. 28 divided by two leaves us
with 14. Another even number! I’m gonna divide by two
again. 14 divided by two is seven. We now recognize that seven is
a prime number. And so that’s the end of this
step. 28 equals two times two times
seven. And we prefer to write it with
exponents which leaves us with 28 equals two squared times seven.

Our next example: Find the
prime factorization of 468.

You might be thinking that 468
is a really big number. Is it going to be super hard to
find the prime factorization for 468? But the answer is no. We’re going to follow the same
procedure. And it will be no different
than finding the prime factorization for other numbers, other smaller
numbers. Okay! Then let’s use the factor tree
method and find the prime factorization here. Again, we recognize that this
is an even number. So you can automatically start
with two. Two times 234 equals 468. Two is a prime number. So this branch is finished.

234 is an even number. Let’s divide 234 by two. Two times 117 equals 234. Two is a prime number. This branch is finished. Now we need some factors of
117. If you don’t immediately
recognize what the factors of 117 are, the best thing to do is try to check
common prime factors. For example, we know that this
is an odd number and not divisible by two. The sum of the digits one, one,
seven is nine, which makes this divisible by three.

So our next step would be to
divide 117 by three. Three times 39 equals 117. Three is a prime number. This branch is finished. I’m gonna move the thirty-nine
over here to give us a little bit more space. What two factors multiply
together to equal 39? It’s pretty easy to spot that
39 is divisible by three. 39 divided by 13 is three. Three is a prime number. This branch is finished. 13 is also prime, which means
we’re finally down to all prime factors.

The end of each branch is a
prime factor. We’re gonna put them all
together to make the prime factorization. We get 468 is equal to two
times two times three times three times 13, for a final answer with exponents of
two squared times three squared times 13 equals 468. And it’s not so bad after
all.

And finally, here are just a few
tips for finding prime factorization. Number one: use the method that
works for you. If you prefer dividing by prime
factors, that’s great! You can find the answer by dividing
by prime factors. If you prefer using the factor tree
and that works for you, use that method. And secondly, if you get stuck and
you’re not sure what factors to check for, check for larger prime numbers. Try dividing the number you’re
factoring by 13, 17, 19, or other prime numbers. And third, just practice. Recognizing what factors are in
numbers comes with practice. You’ll get faster and more accurate
at checking for factorization with practice.