The first step in learning about prime factorization is understanding what it means. When students perform prime factorization, they must find the lowest factors in a number. These numbers must all be prime numbers. Prime numbers are not hard to find if the numbers are low, but if the numbers are high, they are difficult to spot.
There are several tricks teachers use to illustrate easier ways to tell if a number is a prime number or not. The first way to tell is based on if the number is even or odd. Even numbers are always divisible by 2 and therefore, if the number is even and is higher than 2, it is not a prime number. To tell if a number is divisible by 3, add up the digits in the number, and if the answer is a multiple of 3, the number is not prime and can be divided by 3. For example, look at the number 120. Add the digits 1 + 2 + 0. This equals 3; therefore, the number is divisible by 3 and is not a prime number. Find numbers that are divisible by 5 by looking at the last number. If it is a 0 or a 5, it is not a prime number because it is divisible by 5.
Illustrate prime factorization by explaining several problems on the board. Divide the class into two groups. Write a problem on the board and call one person from each team to the board. The person that completes the problem first earns a point for his team. Continue the game as long as you desire.
Teachers commonly use factor trees as a game for teaching prime factorization. Prime factorization is best illustrated through a factor tree. For this activity, place a number at the top of the page. From this number, find two numbers that, when multiplied, equal this number. Place two small lines pointing down from the top number to each of these numbers. For each of these numbers, do the same thing until the numbers are all prime. After you complete the exercise, the work will look like a tree and the bottom numbers will be the prime factorization of the number. For example, place the number 180 on the top of the page. Below it, draw two lines to connect the next numbers, which could be 3 and 60. The number 3 is prime, so that line stops. For the number 60, add two lines with the numbers 3 and 20. From the number 20, write 4 and 5 and from the 4, write 2 and 2. The problem is complete; the answer is found by circling each prime number and writing it out. The answer is 3 times 3 times 5 times 2 times 2.