“Factor” is a term you may have come across while prepping for your GRE. For example, perhaps you were asked to break a number down into its factors or prime factors, maybe even to determine the total number of factors of the number. We’ll get some practice with these kinds of questions in this article, but let’s first discuss what exactly a factor is.


A factor is a number that divides evenly into another number, leaving no remainder. More formally, we can say that if x and y are integers and x/y = integer, then y is a factor of x. To practice this idea, let’s look at the factors of a couple of numbers. For instance, suppose we were asked the following:

What are the factors of 12?

We can see that 1, 2, 3, 4, 6, and 12 are all factors of 12 because they all divide evenly into 12 with no remainder.

What are the factors of 18?

We can see that 1, 2, 3, 6, 9, and 18 are all factors of 18 because they all divide evenly into 18 with no remainder.

If you are struggling to quickly determine all the factors of a particular number, you can perform the following steps.


As an example, let’s determine the factors of 20.

Step 1: Begin with 1 and the number itself. These are factors of every integer. Thus, the first two factors of 20 are 1 and 20. Note that 1 and 20 both evenly divide into 20 because 1 times 20 is 20.

Step 2: Count up from 1, checking whether each integer is a factor of the given number. Stop as soon as you reach a repeated factor.

The next integer after 1 is 2. Since 20/2 = 10, we can say that 2 divides evenly into 20 and that 2 and 10 are factors of 20. Note that 10 also divides evenly into 20 because 20/10 = 2.

Next, we check 3. Since 3 does not divide evenly into 20, we can say that 3 is not a factor of 20.

Moving on to 4, since 20/4 = 5, we can say that 4 and 5 are factors of 20.

Since 20/5 = 4, we can say that 5 and 4 are factors of 20. However, since we have now found repeated factors, we can stop.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

Now, let’s discuss prime factorization.


We now understand how to find all of the factors of a particular number. However, we also need to know how to break a number down into its prime factors. This process is called “prime factorization.” As we may recall, a prime number is an integer greater than 1 that has no factors other than 1 and itself. For example, 2, 3, 5, and 7 are all prime numbers because the only numbers that will divide evenly into them are 1 and themselves. A simple way to find the prime factors of a number is with a factor tree. Let’s use the number 56 as an example.