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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Factors, Multiples and Primes

### Statement Snap

### Factors and Multiples Game

### Gabriel's Problem

### Factors and Multiples Puzzle

### American Billions

### Sieve of Eratosthenes

### Multiples Sudoku

### How Much Can We Spend?

### Product Sudoku

### Diminishing Returns

### Alison's Quilt

### Counting Factors

### Route to Infinity

### Power Mad!

### Stars

### Funny Factorisation

### Differences

### Divisibility Tests

### Beelines

### Latin Numbers

### Take Three from Five

### Expenses

### Shopping Basket

### Factors, Multiple and Primes - Short Problems

### LCM Sudoku

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

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Age 7 to 14

Challenge Level

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

Age 7 to 16

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

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...

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

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?

Age 11 to 16

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

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.

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?

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?

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?

Age 11 to 16

This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.

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?

Age 14 to 16

Challenge Level

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

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?

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?

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?

Age 11 to 16

A collection of short problems on factors, multiples and primes.

Age 14 to 16

Challenge Level

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

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