Question

how to find the prime factorization of a number

Answer 1

http://www.mathsisfun.com/prime-factorization.html
check this site out. hope it helps you... sorry if i doesn't

Answer 2

Let's try as an example, 35.
As the article says, start with the smallest prime number.
35 isn't even and can't be divided by 2 so we move up to 3.
35/3 = 11.6666 so 3 is not a factor
Next prime number is 5 and 35/5 = 7
5 is a factor and 7 remains which is also a prime number so
the prime factorization of 35 = 5 * 7

Answer 3

Take any number, X and determine what two numbers (other than 1 and X) can multiply to get you that number, say these two numbers are a and b. Then do the same for a. What two numbers will multiply to give you a. Do this also for b. Continue until you can't find any more such factors. All the numbers you found are prime numbers, these are the prime factors of your original number, X.

For example. Let X=100. Choose any two numbers that multiply to give you 100, say 2*25. Now take 2. What are two numbers that multiply to give you 2, but are not 1 or 2. You can't find any, so 2 is prime. Next number: 25. Two numbers that multiply to give you 25 are 5*5. Now find two numbers that multiply to give you 5. There is only 1 and 5, so 5 is a prime number.

Combine these results: \(X=2\times5\times5=2\times5^2\). This is the prime factorization of 100. Eventually, you'll be able to do this in your head.

Good Luck!