Myriora Maths › Maths foundations › Chapter 6: Factors, multiples and primes

Why isn't 1 prime?

Ages 7–9Chapter 6 · Lesson 4

In this lesson

A prime number has exactly two different factors: one and itself.
One has only one factor, so it isn't prime.
Leaving one out keeps just one answer for every factor tree.
And two is the only even prime.

Your turn

How many prime numbers are there from one to ten?

Show the answer

The primes up to ten are two, three, five and seven. One isn't prime, and nine isn't either. That's four primes!

The common mistake

Here's a question that catches lots of people. Is one a prime number? Some people say yes, because it only divides by one and itself. But for one, one and itself are the same number! It has only one factor, and a prime needs exactly two.

Try it at home

List the numbers from 1 to 20 together and sort them into primes and not primes. Where does 1 go, and why?

Read the whole lesson

Hello, and welcome to Myriora Maths! Is one a prime number? Lots of people think it is. After all, it only divides by one and itself! But mathematicians say no. Let's find out why.

Here's the exact rule. A prime number has exactly two different factors: one, and itself. Not one factor, and not three. Exactly two.

Let's count some factors. Two has the factors one and two: that's two factors, so it's prime. Seven has one and seven. Prime! Six has one, two, three and six: four factors, so it's not prime. And one? Its only factor is one. That's just one factor, not two. So one is not prime!

But why did mathematicians choose this rule? Think about factor trees. Twelve is two times two times three, and that's the only way to break it into primes. If one were prime, we could also write one times two times two times three, or one times one times two times two times three, for ever! Leaving one out means every number breaks into primes in exactly one way.

Here's another surprise: two is a prime number. It's the only even prime! Every other even number divides by two, so it has more than two factors.

Let's try one together. Is nine a prime number? How many factors does it have? Say it out loud!

Nine has three factors: one, three and nine. That's more than two, so nine is not prime! Odd numbers aren't always prime.

Your turn! How many prime numbers are there from one to ten? Pick the right card. You've got fifteen seconds, or pause the video. Go!

Time's up! The primes up to ten are two, three, five and seven. One isn't prime, and nine isn't either. That's four primes!

Quick review. A prime number has exactly two different factors: one and itself. One has only one factor, so it isn't prime. Leaving one out keeps just one answer for every factor tree. And two is the only even prime. See you next time!