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Prime numbers are special natural numbers greater than 1 that have exactly two factors: 1 and themselves. This means a prime number can be divided evenly only by 1 and itself, making it unique in the number system. For example, 2, 3, 5, and 7 are prime numbers often used in Maths.

Understanding prime numbers is important because they are the building blocks of all numbers. Every number can be written as a product of primes, which helps solve maths problems in GCSE and A-Level Maths.

 

Definition of Prime Number

A Prime Number is a natural number greater than 1 that has exactly two factors: 1 and itself. This means it can only be divided evenly by these two numbers, no more, no less.

For example, the number 7 is a prime number because only 1 and 7 divide it without a remainder. Prime numbers are unique they cannot be broken down into smaller factors, making them fundamental in many areas of maths.

 

Examples of Prime Numbers

Prime numbers are special numbers with only two factors: 1 and themselves. Some of the prime numbers up to 100 are 2, 3, 5, 7, 11, and 13.

Here is a list of 25 prime numbers up to 100:

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.

These numbers are essential in maths as building blocks for other numbers and appear.

Learning these examples helps you recognise primes quickly and solve maths tasks easily.

 

Prime Number vs Composite Number

Prime numbers and composite numbers are two important types of natural numbers that you will study in Maths. Understanding the difference helps build a strong foundation for many math concepts like factorisation and divisibility. Simply put, prime numbers have only two factors, while composite numbers have more than two.

Prime numbers cannot be divided evenly by any number except 1 and themselves. Composite numbers, on the other hand, can be divided evenly by numbers other than 1 and themselves. Recognising this difference makes it easier to solve problems and understand the structure of numbers.

 

Feature

Prime Number

Composite Number

Number of factors

Exactly 2 (1 and itself)

More than 2

Smallest example

2

4

Can it be even?

Only 2 is even

Can be even or odd

Examples (1–20)

2, 3, 5, 7, 11, 13, 17, 19

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20

Prime factorisation

Only itself

Multiple prime factors

Divisibility pattern

Divisible only by 1 and itself

Divisible by several numbers

 

How to Check If a Number Is Prime

Checking if a number is prime is easier than it seems. It involves simple division tests to find if the number has only two factors: 1 and itself. This skill helps students quickly identify prime numbers in their maths studies.

To check if a number is prime, follow these steps:

  1. Ensure the number is greater than 1 (numbers 0 and 1 are not prime).
  2. Find the square root of the number (we only test divisors up to this value for efficiency).
  3. Divide the number by all integers from 2 up to the square root.
  4. If the number is divisible by any of these, it is not prime.
  5. If none divide the number evenly, it is a prime number.

For example, to check if 17 is prime, test divisibility by 2, 3, and 4 (since √17 ≈ 4.1). 17 is not divisible by any of these, so it is prime. But for 18, it is divisible by 2 and 3, so it’s not prime.

This method is quick and perfect for all levels of maths learners.

Prime Numbers in Real Life

Prime numbers play a big role in everyday life, far beyond the classroom. They help keep our online information safe and make computers work more efficiently.

Here are some real-life uses of prime numbers:

  1. Encryption and Cybersecurity: Prime numbers secure credit card and bank information through complex codes.
  2. Computer Algorithms: They optimise how data is stored and accessed, making processes faster.
  3. Nature: Some animals, like cicadas, rely on prime-numbered life cycles to avoid predators.
  4. Music and Technology: Prime numbers help reduce sound distortion and improve signal transmission.

If you have any questions about prime numbers or need expert guidance in maths, MathsAlpha is here to help. Our qualified tutors specialise in GCSE and A-Level Maths, supporting students from Year 7 to Year 11.

Looking for maths classes for your child? MathsAlpha offers personalised, expert tutoring designed to boost confidence and improve results. Contact us today to give your child the best opportunity for success.

Mail us at info@mathsalpha.com or call +44 7834 229046 for Maths classes in the UK.

Frequently Asked Questions

Prime numbers between 1 and 100 are those only divisible by 1 and themselves. Some examples include 2, 3, 5, 7, 11, 13, up to 97. There are 25 primes in this range.

1 is not prime because it only has one factor, itself. Prime numbers must have exactly two factors: 1 and the number itself.

No, prime numbers are always positive natural numbers greater than 1. Negative numbers do not qualify as prime.

Yes, grade 6 is a strong pass, roughly equivalent to a high B in the old grading system.

2 is prime because its only factors are 1 and 2. It’s the smallest and only even prime number.

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