Let’s learn about prime factorization. First, let’s do some backtracking a bit and review vocabulary.

Note: The BIGGEST reason children fail tests is because they DON’T know math terms! Knowing math terms is SO important! Learn the terms. Use them correctly. Know what the vocabulary means.

Any positive integer with EXACTLY two factors is a prime number. In other words, a prime number is a positive integer that has exactly two factors: 1 and itself.

Factors are the numbers you multiply together to get the product. Algebraically it would look like this: a • b = c where a and b are the factors and c is the product.

Is 4 prime? 7? 11? or 15?

First, try to find all of the factors of the numbers. For simple numbers like the ones above, it isn’t too hard.

4 = (1, 2, 4)

7 = ( 1, 7)

11 = (1, 11)

15 = (1, 3, 5, 15)

So, based on our definition, the prime numbers are 7 and 11 because they have exactly two factors. But, 4 and 15 are not. What would we call these numbers since they have three or more factors?

Composite numbers are positive integers that have THREE or more whole number factors.

What if you want to find all of the factors of a number? How could you do it? EASY! Use Prime Factorization! In fact, get out your Sieve of Eratosthenes to help you. This tool is a great one because it can help provide a way for you to check for prime numbers.

Prime Factorization is a method used to find all of the prime factors of a number. It utilizes a tree diagram for organizing your factors.

Let’s try it using the number 24.

If you recall your basic facts, you can start with 4 times 6. You could start with a variety of combinations: 3 times 8 or even 12 times 2 but for this example, we'll use 4 times 6.

Look at your Sieve of Eratosthenes as this is an excellent math tool. It is going to help you now as you prime factor the number 24. Note how both 4 and 6 are composite numbers. This means you need to continue your factor tree branches until you get down to only the prime factors for 24.

Check your Sieve. Are the numbers at the end of your branches now all primes? If yes, then circle them.

(When they're not, then you just keep extending the branches…)

Now, re-write the number. Normally, primes are written in increasing order from left to right and exponential notation is used, if necessary.

That's it! You did it!

Want to practice on your own? Then click Prime Factorization Practice to download a worksheet to try. You should get out your Sieve of Eratosthenes to help you out with those prime numbers…

If you want even MORE practice, then click More Prime Factorization Practice.

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