What is a prime?

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Key points

  • A number is a number that has exactly two - itself and 1. There are an infinite number of prime numbers.

  • Numbers that have more than two factors are called . They can be expressed as a of prime numbers.

  • The number 1 is not a prime number or a composite number. It is often referred to as a unit.

  • The only even prime number is 2. All other even numbers can be divided by 2

  • Knowledge of prime numbers helps in understanding of highest common factor (HCF), lowest common multiple (LCM) and product of prime factors.

Knowledge of prime numbers is helpful in supporting understanding of (HCF), and .

Prime numbers activity

Play this game to find all the prime numbers up to 100.

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What is a prime number?

  • A prime number has exactly two – itself and 1. This means it also only has one .
  • A prime number is only divisible by itself and 1

Prime numbers are used to:

  • find the (HCF) and of two or more numbers.
  • break down a into a product of its prime factors.

Examples

Factors of two: one and two. Factors of nineteen: one and nineteen. Factors of thirty-one: one and thirty-one.

Every prime number has exactly two factors – 1 and itself. This is one factor pair. 2, 19 and 31 are prime numbers. The factors of 2 are 1 and itself (2). The factors of 19 are 1 and itself (19). The factors of 31 are 1 and itself (31)

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Question

Which numbers between 80 and 90 are prime numbers?

80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90

The only prime numbers between 80 and 90 are 83 and 89

83 = 1 x 83

89 = 1 x 89

All the other numbers have more than two factors.

A prime number has exactly two factors, itself and 1

Practise prime numbers

Practise what you've learned about prime numbers with this quiz.

Quiz

Real-world maths

Prime numbers are important in creating digital security systems (cybersecurity).

The prime numbers used to secure data through encryption are extremely large. You can multiply two very large prime numbers together, but it is difficult to break that number back down and find the factors.

This is part of what keeps information secure.

Prime numbers are used in cybersecurity.