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### Course: Pre-algebra > Unit 1

Lesson 3: Prime factorization# Prime factorization

This video explains the concept of prime numbers and how to find the prime factorization of a number using a factorization tree. It also shows how to write the prime factorization using exponential notation. A prime number is a number that is only divisible by itself and one. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- At2:07he figures out that 75 is divisible by 3, by adding 7 to 5. I've never heard anyone do this and I'd like to know why this works this way. Is there a video on this topic?(155 votes)
- what happens if we need to deal with very large numbers like 188,796? do we do the same thing?(59 votes)
- Yes...

Word of Wisdom: there's no shortcut of prime factorization...

You have to do same thing...

Although it will took a long time.

But like TI-85... you can do prime factorization on your calculator.

Only few calculator can do prime factorization...

Have fun(47 votes)

- how do you type an exponent on a keyboard?(36 votes)
- ^←this is exponential mark

2^6 (2 to power of 6)

3^123456 (3 to power of 123456)

Have fun!!!!!!!!!!

★○●◎◇◆□■△▲▽▼◁◀▷▶♤♠♡♥♧♣◈▣◐◑▒▤▥▨▧▦▩☜☞¶†♩♪♬(15 votes)

- Isn't a "Not Prime" number called a composite?(32 votes)
- Technically no in one case, the number 0. 0 is neither a prime nor composite number it is undefined in this are of math.(2 votes)

- is 1 a prime number

yes

or

no(13 votes)- We do not want 1 to be a prime number. Otherwise the prime factorization of a number would not be unique, since 1 times anything is that anything.

Then the prime factorization of, let's say 200, would be 2^3 * 5^2, but also 1^2 * 2^3 * 5^2, or even 1^2013 * 2^3 * 5^2.(8 votes)

- - p r i m e f a c t o r i z a t i o n -(13 votes)
- What is the biggest prime number?(5 votes)
- There is no biggest prime number. The number of primes is infinite. If you find any prime number there'll always be a bigger prime(11 votes)

- In the video Sal uses prime factorization to figure out 75. I understand what he says just fine...

but when i try to use the same method for 125 i get confused.

7+5 added is 12 and that's divisible by 3

3 x 25 =75 i get it.

now i do 125...i add them up and get 8... which is divisible by 2 and 4... but 125 is not divisible by either 2 or 4.. so i get stuck here.

now i can see just fine that 125 is 5 x 25, and then 5x5=25 so 5x5x5=125, but i want to figure it out by using the same method Sal did.

where am i going wrong?(4 votes)- Adding the digits is just a test of divisibility and you could ONLY use the sum of the digits as a test of divisibility for 3. So when you add the digits of 125, you get 8 which shows that it is not divisible by 3. For 2, the test of divisibility is looking at the last digit. If it is even , then the number is divisible by 2. if it is odd then it is not. I think you'll find videos more on test of divisibility on KA.(6 votes)

- Since 0 and 1 are neither prime nor composite, is there a word that describes what they are?(10 votes)
- I is nither composite or prime so it is "nither"(2 votes)

- I need help. I can't get it right . Do you mind helping me find another way, so I understand the concept of Prime Factorization?(8 votes)
- cool but this is prime factorization not division but thanks for the info(0 votes)

## Video transcript

Write the prime factorization
of 75. Write your answer using
exponential notation. So we have a couple of
interesting things here. Prime factorization, and they
say exponential notation. We'll worry about the
exponential notation later. So the first thing we have to
worry about is what is even a prime number? And just as a refresher, a
prime number is a number that's only divisible by itself
and one, so examples of prime numbers-- let me write
some numbers down. Prime, not prime. So 2 is a prime number. It's only divisible
by 1 and 2. 3 is another prime number. Now, 4 is not prime,
because this is divisible by 1, 2 and 4. We could keep going. 5, well, 5 is only divisible
by 1 and 5, so 5 is prime. 6 is not prime, because it's
divisible by 2 and 3. I think you get the
general idea. You move to 7, 7 is prime. It's only divisible
by 1 and 7. 8 is not prime. 9 you might be tempted to say
is prime, but remember, it's also divisible by 3,
so 9 is not prime. Prime is not the same thing
as odd numbers. Then if you move to 10,
10 is also not prime, divisible by 2 and 5. 11, it's only divisible
by 1 and 11, so 11 is then a prime number. And we could keep going
on like this. People have written computer
programs looking for the highest prime and all of that. So now that we know what
a prime is, a prime factorization is breaking up
a number, like 75, into a product of prime numbers. So let's try to do that. So we're going to start with
75, and I'm going to do it using what we call a
factorization tree. So we first try to find just the
smallest prime number that will go into 75. Now, the smallest prime
number is 2. Does 2 go into 75? Well, 75 is an odd number, or
the number in the ones place, this 5, is an odd number. 5 is not divisible by 2, so
2 will not go into 75. So then we could try 3. Does 3 go into 75? Well, 7 plus 5 is 12. 12 is divisible by 3, so
3 will go into it. So 75 is 3 times
something else. And if you've ever dealt with
change, you know that if you have three quarters, you have
75 cents, or if you have 3 times 25, you have 75. So this is 3 times 25. And you can multiply this out
if you don't believe me. Multiple out 3 times 25. Now, is 25 divisible by--
you can give up on 2. If 75 wasn't divisible by 2,
25's not going to be divisible by 2 either. But maybe 25 is divisible
by 3 again. So if you take the digits
2 plus 5, you get 7. 7 is not divisible by 3, so 25
will not be divisible by 3. So we keep moving up: 5. Is 25 divisible by 5? Well, sure. It's 5 times 5. So 25 is 5 times 5. And we're done with our prime
factorization because now we have all prime numbers here. So we can write that 75
is 3 times 5 times 5. So 75 is equal to 3
times 5 times 5. We can say it's 3 times 25. 25 is 5 times 5. 3 times 25, 25 is 5 times 5. So this is a prime
factorization, but they want us to write our answer using
exponential notation. So that just means, if we have
repeated primes, we can write those as an exponent. So what is 5 times 5? 5 times 5 is 5 multiplied
by itself two times. This is the same thing as
5 to the second power. So if we want to write our
answer using exponential notation, we could say this is
equal to 3 times 5 to the second power, which is the
same thing as 5 times 5.