Prime Numbers, Factor Trees, and Prime Factorization

Prime Numbers

One key that I have learned to really appreciate in finding factors is to know the prime numbers. A prime number is a number that cannot be divided among 2 numbers (excluding the number 1). 6 is not prime because it can be divided by 2 and 3. 2 cannot be broken down any more and neither can 3. The prime factors of the number 6 are 2 and 3. There are only a certain number of prime numbers and those are the ones we are looking for.

This chart will help for finding prime numbers quickly:

Video on polishing up your prime number skills...

Factor Trees and Prime Factorization

This is a wonderful tool that I have used over and over in factor finding, and have even found other uses for it just for fun. It's quick and easy to do on paper without a calculator if the numbers aren't to big, but if they get a little bigger you may want to use a calculator. The purpose of this exercise is to find the prime numbers of any given number by breaking in down piece by piece. My favorite way to do it is to see if the number can first be divided by 2. If not, then maybe 3, or 5.  Let's take the number 246...

246

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2  123

246 divided by 2 gives us 123..

2 cannot be broken down anymore because it's a prime number, but 123 can be..
 Lets keep going...

246
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2  123

    /\

     3 41

123 can be broken down to 3 divided by 41.
Since 41 cannot be broken down any more we consider it a prime number.
The prime factorization of the number 246 is 2x3x41.
This is not only a great tool just to have and to know how to do, but it will come in handy for other problem solving needs in the future, when you want to learn quick and easy ways how to find Least Common Multiples or Greatest Common Divisors. It's also just good to know the breakdown of any number, and enhances your math skills in general.

Click here for some math game ideas for learning factor trees in the classroom!