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• A prime number will only have two factors.

• A prime number will only be divisible by 1 and by itself.

• Prime numbers are often used in encryption and making codes.

How do we know if a number is a prime?

One way to test if a number is prime, is to use some playing cards. The number of cards we need depends on what number we are testing.

Firstly, arrange the cards so that they form a single column. Using the same amount of cards try to form a perfect rectangle with two columns of cards. If you are able to form a perfect rectangle that does not have a height of one, then your number is not prime.

Which of the numbers, 1 to 12, are prime?

• 1 is not prime because it does not have two factors.
• 2 is prime as it forms a rectangle that is 1 card by 2. So 2 only has two factors.
• 3 is prime as this forms a rectangle that is 1 card by 3. It has only two factors.
• The next number is 4. We can see that 4 is not prime. This is because you can form a 2 x 2 rectangle, which has 2 columns.
• 5 is prime as it forms a rectangle that is 1 card by 5. It only has two factors.
• 6 is not prime as it can form a rectangle that is 3 x 2.

Can you work out the remaining primes between 7 and 12?

Where are primes useful?

Banks use encryption and codes to have higher level security within their business. Prime numbers are multiplied together to generate extremely large encryption keys. It can take computers days or even weeks to calculate these keys!

Where next?

Discover more maths topics on Bitesize.

Maths