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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?

• At he 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?
• what happens if we need to deal with very large numbers like 188,796? do we do the same thing?
• 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
• how do you type an exponent on a keyboard?
• ^←this is exponential mark
2^6 (2 to power of 6)
3^123456 (3 to power of 123456)

Have fun!!!!!!!!!!
★○●◎◇◆□■△▲▽▼◁◀▷▶♤♠♡♥♧♣◈▣◐◑▒▤▥▨▧▦▩☜☞¶†♩♪♬
• Isn't a "Not Prime" number called a composite?
• Technically no in one case, the number 0. 0 is neither a prime nor composite number it is undefined in this are of math.
• is 1 a prime number
yes
or
no
• 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.
• - p r i m e f a c t o r i z a t i o n -
• What is the biggest prime number?
• 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
• 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?
• 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.