Factors, Multiples and Primes

This  collection of resources supports the teaching of factors, multiples and primes in secondary mathematics.


Here are some favourite activities selected by the NRICH team.


  • Factors and Multiples Game A game in which players take it in turns to choose a number. Can you block your opponent?
  • Factors and Multiples Puzzle Using your knowledge of the properties of numbers, can you fill all the squares on the board?
  • Gabriel’s Problem Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
  • Dozens Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
  • Stars Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
  • Take 3 From 5 Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
  • Counting Factors Is there an efficient way to work out how many factors a large number has?

These are just a few of the activities on Factors, Multiples and Primes  that you can find on the NRICH curriculum pages.





The activities below, taken from the STEM Learning website, complement the NRICH activities above.

Links and Resources

Factors, Multiples and Primes

A series of videos from MathsMaster that introduce and explore the concept of factors, multiples and primes respectively.

publication year
2010 to 2019

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Number Types

This Virtual Textbook resource contains an interactive version of the prime number sieve to complement the NRICH activity Sieve of Eratosthenes.

More of Eratosthenes' mathematical exploits can be found on p40 in the from Century Maths textbook People Patterns / Cultures Count

publication year
2000 - 2009

3 files



Properties of Number

This SMILE resource contains games, investigations, worksheets and practical activities supporting the teaching and learning of the properties of number, and a booklet 'Squares and Primes'.

Properties of number pack one contains sixteen work cards with a wide variety of activities covering odd and even numbers, multiples, rectangle numbers, and factors.

Properties of number pack two contains twelve work cards with activities requiring students to explore prime numbers, find patterns in multiples , use the sieve of Eratosthenes to find prime numbers, investigate triangle numbers, and use factors.

Properties of number pack three contains fourteen work cards with activities involving multiplication patterns, finding prime factors, divisibility problems, number challenges, finding highest common factors and lowest common multiples, investigating quadratics and primes, rational and irrational numbers, and proof by contradiction.

Squares and Primes is a booklet investigating prime numbers, primes and factorials, proof, Euclid and Greek mathematics.


publication year
2000 - 2009

4 files



Factors and Multiples

If you would like more resources covering factors and multiples, this package contains a variety of resources from the National STEM Learning Centre collection.

The resources support student understanding of prime numbers and how they can be used with reference to common factors and common multiples. The collection includes resources from CIMT, Century Maths and more.

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