Prime Factorization


This tutorial is on prime factorization and how to do it step by step. This is a really important process and one that can be very confusing at times. One can easily mess up and get the wrong answer. So let’s jump right in and learn the concept of factorization!

Sample Problem

6 x 4 = 24


what is prime factorization?
Prime factorization is the lowest number that a number can go into.
Example. the prime factorization of 8 is

                                   4  2

two is a prime factor because 1 and itself are the only two numbers that can go into it. 4, on the other hand, is not so here’s how we break it down.

first, ask yourself what goes into 4.
answer 1, 2 and 4

                                  4  2 
                                2  2        

Answer 2x2x2=8

Now that you know how to get a prime factor lets try a whole equation.

The 1st equation is 6 x 4 = 24
so let’s break it down let us start with 6

step one: what are the factors of 6 1,2,3, and 6
choose either 3, 2 or 6,1

step two simplify each factor 3,2 are prime factors but 6, 1 are not. To find the multiples that equal 6 which are 3, 2

                             6     6
                            /\    /\
                           3  2  6  1    
                               3 2 

so, either way, you will get the same answer of the prime factor being 3,2 the first part of the equation is 3×2

Part two: find the factors of 4 which are 2,2 and 4,1
choose one of the sets of factors I will show both below

                               4          4  
                              /\         /\ 
                             2  2       4  1 
                                      2 2  

The first set 2,2 are already prime factors as 1 and itself are the only two numbers that go into it. On the other hand 4, 1 are not but once factored you get the same answer of 2,2
the second part of the equation is 2×2

Step Three: write the equation with both parts
which is the same as 6×4=24 but simplified

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