First Topic: Prime Factorization

This is the first topic I've ever covered here, so I hope you find this helpful and informative!
The topic is prime factorization. Now, for my "topics", I will cover a range of things of all grade levels and subjects. If you know how to do this already, that is O K. This is kind of a test post. However, if you don't know about this topic, then I hope you can benefit from it.

Prime factorization is where you break a number down into its prime factors. A factor is any number multiplied by another number to equal a product.
Examples of factors:

2 * 3 = 6
The factors are 2 and 3.

To prime factorize a number, you can use the branching method or the stacking method.

Branching:

I can't really type this, but I can put a picture:

So, basically, you break the original number down two factors at a time.
Let's try 24.

12 and 2 are two factors, or "branches" of 24.

                 24
       12                 2
2 is prime, so you can't do anything to it. Now let's look at 12.

4 and 3 are two factors of 12

                   12
            4             3
3 is prime, so let's look at 4.
4 has two factors: 2 and 2.

            4
      2            2

So, go through your final "tree" and find all prime factors.

                            24
                   12               2
             3            4
                     2           2
So, the prime factorization of 24 is:

3 * 2 * 2 * 2

The other method is stacking.
You write the number you are trying to factorize at the top. In this case, 24.

                                    24
Next, draw an inverted long division sign on the number.

                                |24
Kind of like that.
Next, you write one prime factor of the number outside the "stack".

                            2|24
Now, divide 24 by the prime first prime factor, and write the result under 24, and form another "stack".

                            2|24
                                |12
Repeat until you cannot divide the number inside the stack any more.

                            2|24
                               2|12
                                  2|6
                                     3
The numbers outside of the stacks are the prime factors.




Here are some sample problems:

1) 32
2) 76
3) 15
4) 51
5) 145
6) 108
7) 225
8) 81
9) 102
10) 1000


If you have any questions, please email me at inquirzoom@gmail.com.

I hope that helped!