User:JustBerry/Math/Prime Factorization/sandbox

Status: Work In Progress

[http://en.wikipedia.org/wiki/Integer_factorization]

Introduction

Definition of Prime factorization

• Beginner: "'Prime Factorization' is finding which prime numbers multiply together to make the original number."
• Intermediate: "Prime factorization is to write a composite number as a product of its prime factors."
  

How to do a prime factorization

There are several methods to doing a prime factorization. The 'Factor Tree' method is one of the most common methods to finding a prime factorization.

• "Factor Tree" Method: This method represents the prime factors of a positive integer in a "family tree layout/diagram" (See right images). There are two 'sub methods' to finding the prime factors in the 'Factor Tree' method. The first 'sub method' is to split the original integer into two other factors: one being the smallest, divisible factor of the original integer and other being the quotient of the integer divided by the other factor (See first photo). Since the former factor is already a prime number, one prime factor has been already found. If the other factor is a prime number as well, then all of the possible prime factors for the original integer have been found. If not, then the number is not a prime factor, therefore needs to be 'broken down' even further. Let's take the example on the right. '21' is further broken down in 3 and 7. The same method is applied as the method to breaking the original integer into two factors (see above). The other method is to split the original integer into two positive integers that are not too far apart.

Finding the prime factorization of 42 via the 'Factor Tree method'

Finding the prime factorization of 42 via the 'Factor Tree method'

Prime Factorization Media

http://www.khanacademy.org/math/arithmetic/factors-multiples/prime_factorization/v/prime-factorization

Prime Factorization Practice

http://www.khanacademy.org/math/arithmetic/factors-multiples/prime_factorization/e/prime_factorization

http://www.mathplayground.com/factortrees.html