Before we get into prime factorization
Factors are the numbers you multiply together
to get another number as the product.
And since you've worked with prime numbers before,
you should remember...
Mathematicians call prime numbers...
In other words...
We call these...
the prime factors of a number.
I'll show you how this idea stacks up...
2 is prime
3 is prime
4 comes from 2x2
5 is prime
We get 6 from 2x3
7 is prime
8 comes from 2x2x2
9 is from 3x3
We get 10 from 2x5
11 is prime
12 is from 2x2x3
13 is prime
14 is from 2x7
And we get 15 from 3x5
To do a prime factorization
we can use a factor tree
to help us split each composite number apart
into its prime factors.
Let's do an example
We split 18 into factors
until we can't split anymore
I'm using red for prime numbers
and blue for composite numbers
I say to myself:
18 comes from 2x9
I circle 2 as a prime number.
I'll come back to it later.
9 is a composite number
so I split it down.
I get 9 from 3x3
3 is a prime number
So I circle both of them as well.
Next to the factor tree
It's correct, but it's not QUITE finished...
To do a really GREAT job
on prime factorization
we show a factor that is repeated
by using EXPONENTS. We call it...
It sounds fancy, but it's easy enough.
Check it out: How many 3s have I got?
So I say...
"to the power 2"
because 3 is used twice
It makes the final answer very tidy.
Notice that I listed the prime factors
from smallest to largest.
That is the standard way of listing prime factors,
and you should do that too.
I could have done it differently and said...
18 is from 3x6
6 is from 2x3
I still get the SAME prime factors
...and then it's. your turn.
This time I have two composite numbers to work on.
4 is from 2x2
2 is prime
I circle them both and move on to the 12.
12 comes from 2x6
and 6 is from 2x3
I circle all the primes
I found all the primes
And for a GREAT final answer
we use our exponential notation
to tidy up those repeated factors.
2 came up four times.
So we say 2 to the power 4...
And that's all you need to do.