Factors, multiples and primes

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

problem

Favourite

Statement snap

Age

7 to 14

Challenge level

You'll need to know your number properties to win a game of Statement Snap...

problem

Favourite

Xavi's t-shirt

Age

7 to 16

Challenge level

How much can you read into a t-shirt?

game

Favourite

Factors and multiples game

A game in which players take it in turns to choose a number. Can you block your opponent?

problem

Favourite

Dozens

Age

7 to 14

Challenge level

Can you select the missing digit(s) to find the largest multiple?

problem

Favourite

Diminishing returns

Age

11 to 14

Challenge level

How much of the square is coloured blue? How will the pattern continue?

problem

Favourite

Sieve of Eratosthenes

Age

11 to 14

Challenge level

Follow this recipe for sieving numbers and see what interesting patterns emerge.

problem

Favourite

Multiple surprises

Age

11 to 16

Challenge level

Sequences of multiples keep cropping up...

problem

Favourite

Gabriel's problem

Age

11 to 14

Challenge level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

problem

Favourite

Number families

Age

11 to 14

Challenge level

How many different number families can you find?

problem

Favourite

American billions

Age

11 to 14

Challenge level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

problem

Favourite

Factors and multiples puzzle

Age

11 to 14

Challenge level

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

problem

Favourite

Multiples Sudoku

Age

11 to 14

Challenge level

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

problem

Favourite

How much can we spend?

Age

11 to 14

Challenge level

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

problem

Favourite

Alison's quilt

Age

11 to 14

Challenge level

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

problem

Favourite

Counting factors

Age

11 to 14

Challenge level

Is there an efficient way to work out how many factors a large number has?

problem

Favourite

Funny factorisation

Age

11 to 16

Challenge level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

problem

Favourite

Take three from five

Age

11 to 16

Challenge level

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

problem

Favourite

Stars

Age

11 to 14

Challenge level

Can you work out what step size to take to ensure you visit all the dots on the circle?

problem

Favourite

Product Sudoku

Age

11 to 16

Challenge level

The clues for this Sudoku are the product of the numbers in adjacent squares.

problem

Favourite

Route to infinity

Age

11 to 14

Challenge level

Can you describe this route to infinity? Where will the arrows take you next?

problem

Favourite

Power mad!

Age

11 to 14

Challenge level

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

problem

Favourite

Differences

Age

11 to 14

Challenge level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

problem

Favourite

Shopping basket

Age

11 to 16

Challenge level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

problem

Favourite

Beelines

Age

14 to 16

Challenge level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

problem

Favourite

Filling the gaps

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?

problem

Favourite

Expenses

Age

14 to 16

Challenge level

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

problem

Favourite

LCM Sudoku

Age

14 to 16

Challenge level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

problem

Favourite

Latin numbers

Age

14 to 16

Challenge level

Can you create a Latin Square from multiples of a six digit number?

You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Factors, multiples and primes

Statement snap

Xavi's t-shirt

Factors and multiples game

Dozens

Diminishing returns

Sieve of Eratosthenes

Multiple surprises

Gabriel's problem

Number families

American billions

Factors and multiples puzzle

Multiples Sudoku

How much can we spend?

Alison's quilt

Counting factors

Funny factorisation

Take three from five

Stars

Product Sudoku

Route to infinity

Power mad!

Differences

Shopping basket

Beelines

Filling the gaps

Expenses

LCM Sudoku

Latin numbers