What Are Prime Numbers?

There are lots of different ways to study and classify numbers. Maybe you’ve heard of classifications such as prime and composite numbers. If you’re wondering “what are prime numbers?”, here are some things that you should know about them.

FREE Math Video Lessons from Magoosh! Start here.

what are prime numbers - magoosh

Photo by MichaelJayBerlin

What Are Prime Numbers?

A prime number is one that only has two factors: one and itself. This means that the number can’t be divided evenly by any number but one.

Prime numbers are the building blocks of numbers. You can break down all numbers to prime numbers. There are an infinite number of prime numbers, but they are less frequent as numbers get larger. For these reasons, mathematicians have enjoyed studying and discovering other prime numbers.


So how do you find prime numbers? Let’s look at the numbers up to 100. As Eratosthenes discovered, there are a few multiples that you can look for to weed out the numbers that are not prime numbers. Start with a chart up to 100:

what are prime numbers, chart 1 - magoosh

First, cross out the numbers that are multiples of 2 (hold off on 2):

what are prime numbers, chart 2 - magoosh

Then, skip 5 but remove the rest of the multiples of 5:

prime and composite numbers, chart 3 - magoosh

Next, cross out the multiples of 3 starting with 6:

prime and composite numbers, chart 4 - magoosh

And finally, locate the multiples of 7 (not including 7). Go ahead and cross those out, too:

what are prime numbers, chart 5 - magoosh

Now, look at the numbers that are left. These are the prime numbers to 100. Those numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
If you continue to test for prime numbers beyond 100, see if you can evenly divide the number into groups.

Composite Numbers

If a number isn’t a prime number, it’s probably going to be a composite number. Composite numbers are simply ones that have more than 2 factors. For example, the factors of 4 include 1 x 4 and 2 x 2. Since there are more factors than just one and itself, 4 would be considered a composite number (even if it has only 3 factors: 1, 2, and 4).

Zero and One

Years ago, mathematicians classified zero and one as prime numbers. However, now these numbers aren’t considered to be prime or composite numbers. To be a prime number, a number should have just 2 factors: 1 and itself. However, 1 = 1 x 1. Therefore, 1 only has 1 factor: itself. Therefore, it can’t be a prime or a composite number.

Zero acts in the same way: 0 = 0 x 0. Because it only has 1 factor, 0 is also difficult to classify as either a prime or composite number.

As you study numbers, start by classifying whether each number is a prime or composite number. If it’s a composite number, try to break it down to its prime number factors. Soon, you’ll become a pro with prime numbers. So, when someone asks “what are prime numbers?” you can teach them all about it!

FREE Math Video Lessons from Magoosh! Start here.


  • Jamie Goodwin

    Jamie graduated from Brigham Young University- Idaho with a degree in English Education. She spent several years teaching and tutoring students at the elementary, high school, and college level. She currently works as a contract writer and curriculum developer for online education courses. In her free time, she enjoys running and spending time with her boys!

No comments yet.

Magoosh blog comment policy: To create the best experience for our readers, we will only approve comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! 😄 Due to the high volume of comments across all of our blogs, we cannot promise that all comments will receive responses from our instructors.

We highly encourage students to help each other out and respond to other students' comments if you can!

If you are a Premium Magoosh student and would like more personalized service from our instructors, you can use the Help tab on the Magoosh dashboard. Thanks!

Leave a Reply