Category Archives: Factoring

Grasping the Greatest Common Factor


It feels like just yesterday I was learning about greatest common factors in elementary school. The only difference from learning GCF’s now is that I actually understand it. The greatest common factor is the largest possible number that can divide into a set of numbers equally. An example of this is find the GCF of (24,36), the answer is 12 because 12×2=24 and 12×3=36. There are no larger numbers that divide equally into 24 and 36.

Although the example GCF(24,36) is simple, there is a trick for the more complex problems. For example find the greatest common factor of (2100,3360) seems almost impossible, but I have learned a trick to help speed up the process. Instead of plugging numbers into your calculator you simply need to draw a factor tree for both numbers. The picture provided is what the factor trees should look like.

Once you have the factor trees drawn, you write out the prime numbers for 2100 and 3360. The prime factors of 2400 are 2x2x3x5x5x7, and the prime factors of 3360 are 2x2x2x2x2x3x5x7. The trick to finding the GCF of the 2100 and 3360 is to look at the intersection (overlap) of the numbers. The numbers in read are the overlap (2x2x3x5x7). After you find the intersection, you need to multiply the numbers together (2x2x3x5x7=420). This means that the greatest common factor of 2400 and 3360 is 420. This may look like a lot of work, but it is actually much less work than using your calculator to guess and check numbers.

Facts about Factors


Factors can be intimidating, but there are some tricks that help to understand them. Factors are numbers that are multiplied together to equal the final number. For example in the problem 2×4=8, the factors are 2 and 4. Although these are factors, they are not prime factors. Prime means any number greater than 1, and its only factors are 1 and itself. Some examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, and 43. If we go back to the problem 2×4=8, clearly 4 is not a prime number; therefore, we have to break it down until it is a prime number. To break down 4 into prime numbers we can start by finding a multiple of 4, which is 2 (2×2 = 4). Now we have all prime numbers: 2x2x2=8; this is the same as saying 2×4=8.

Factor trees help to find the prime factors of a number by first obtaining any two factors and then obtaining their factors. This may seem confusing, but it is actually quite simple. For example if we have the number 40, we can start by obtaining any two factors (8×5). Since 5 is already a prime number, we only need to obtain the factors of 8. These factors could be 4×2. Once again, 2 is a prime number; therefore we only need to break down the number 4. The number 4 breaks down into 2×2. Now we have all the prime factors of 40: 5x2x2x2=40. I have provided a picture of a factor tree to help visualize the problem.

A fun game that involves practicing factors is called Roast Turkey. This game helps to gain further knowledge of factors and helps to practice them. The game begins by letting the player choose what level you want. After you choose your level, it explains that you use your keyboard arrows and space bar to navigate “Professor Super”. Once you click the begin button, it will bring up a page that explains factors. Now it is time to begin the game; a question will pop up like: what is not a factor of 25. There will be three uncooked turkeys floating around your screen with different numbers in each one. You have to use the arrows to navigate “Professor Super” and the space bar to “fire” the correct turkey. This is a fun interactive factoring game!