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

Prime numbers

Ages 7–9Chapter 6 · Lesson 3

In this lesson

A prime has exactly two factors: one, and itself.
One is not prime, and two is the only even prime.
And a sieve finds all the primes.

Your turn

Which of these are prime: twenty-one, twenty-three, twenty-seven, or twenty-nine?

Show the answer

Twenty-three and twenty-nine are prime. Twenty-one is three times seven, and twenty-seven is three times nine.

The common mistake

Here's a question that catches lots of people. Are one and nine prime numbers? Some people say yes. But a prime has exactly two factors, and one has only one factor: itself. So one is not prime. And nine isn't prime either, because three times three is nine.

Try it at home

Try to arrange 7 or 11 counters into a rectangle with more than one row. When you can't, the number is prime.

Practise it as a puzzle. In Factor Gems, every gem is a number, and four gems that share a prime factor divide each other down. Spotting factors becomes the way to play.

Play Factor Gems free in your browser

The one-minute version

Read the whole lesson

Hello, and welcome to Myriora Maths! Some numbers can't be made into a rectangle, however hard you try. They're called prime numbers, and they're the building blocks of maths.

Why do primes matter? Many of the secret codes that keep the internet safe are built from huge prime numbers, hundreds of digits long. And in maths, every whole number can be built by multiplying primes.

Try making rectangles. Twelve counters make lots of rectangles: two by six, three by four. But seven counters? The only way is one long row. Seven is prime!

So a prime number has exactly two factors: one, and itself. Two, three, five, seven, eleven, thirteen. Two is the only even prime, because every other even number divides by two.

Let's try one together. Is fifteen a prime number? Can fifteen counters make a rectangle? Say your answer out loud!

Fifteen counters make three rows of five! So three and five are factors of fifteen. Fifteen is not prime. Well done if you said no!

To find all the primes up to fifty, use a sieve. Cross out one. Keep two, and cross out every other multiple of two. Keep three, and cross out its multiples. Then five, then seven. Whatever's left is prime!

Your turn! Which of these are prime: twenty-one, twenty-three, twenty-seven, or twenty-nine? Pick the right cards. You've got fifteen seconds, or pause the video. Go!

Time's up! Twenty-three and twenty-nine are prime. Twenty-one is three times seven, and twenty-seven is three times nine.

Quick review. A prime has exactly two factors: one, and itself. One is not prime, and two is the only even prime. And a sieve finds all the primes. See you next time!