User:JustBerry/Math/Prime Factorization/sandbox

Status: Work In Progress

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

Introduction

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

Prime Factorization of 42 via Factor Tree Method

Definition of doing a 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. 42 was broken down into 2 and 21; since 2 was a prime number, one of the positive integer's factors has already been found. Now, the factor 21 is remaining. 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. In the second image, 42 is broken down into 6 and 7. Although 7 ended up being a prime number, this may not always be the case, especially for larger integers. Since 6 is not yet a prime number, 6 is broken down into 3 and 2. Since these are both prime numbers, and factors, of the positive integer (42), all of the prime factors of 42 have been found.

How to write a prime factorization

A prime factorization is the set of prime factors for a particular positive integer.

2 x 3 x 7 = 42

This is the prime factorization for 42. All of the prime factors of 42 are multiplied to an equation and set equal to the original integer, 42.

2² x 3 = 12

Often times, when a prime factorization has the same prime factor (f) appearing x number of times, the factors can be written as a power f^x

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