# Factors, Multiples and Primes

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

### Statement Snap

##### Age 7 to 14Challenge Level

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

### Factors and Multiples Game

##### Age 7 to 16Challenge Level

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

### Gabriel's Problem

##### Age 11 to 14Challenge Level

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

### Factors and Multiples Puzzle

##### Age 11 to 14Challenge Level

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

### Number Families

##### Age 11 to 14Challenge Level

How many different number families can you find?

### American Billions

##### Age 11 to 14Challenge 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...

### Sieve of Eratosthenes

##### Age 11 to 14Challenge Level

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

### Dozens

##### Age 7 to 14Challenge Level

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

### Multiples Sudoku

##### Age 11 to 14Challenge Level

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

### Multiple Surprises

##### Age 11 to 16Challenge Level

Sequences of multiples keep cropping up...

### How Much Can We Spend?

##### Age 11 to 14Challenge 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?

### Product Sudoku

##### Age 11 to 16Challenge Level

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

### Diminishing Returns

##### Age 11 to 14Challenge Level

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

### Alison's Quilt

##### Age 11 to 14Challenge Level

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

### Counting Factors

##### Age 11 to 14Challenge Level

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

### Route to Infinity

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge Level

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

### Stars

##### Age 11 to 14Challenge Level

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

### Funny Factorisation

##### Age 11 to 16Challenge Level

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

### Differences

##### Age 11 to 14Challenge Level

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

### Divisibility Tests

##### Age 11 to 16

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

### Beelines

##### Age 14 to 16Challenge Level

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

### Latin Numbers

##### Age 14 to 16Challenge Level

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

### Filling the Gaps

##### Age 14 to 16Challenge Level

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

### Take Three from Five

##### Age 11 to 16Challenge 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?

### Expenses

##### Age 14 to 16Challenge 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 16Challenge Level

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

### Factors, Multiple and Primes - Short Problems

##### Age 11 to 16

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

### LCM Sudoku

##### Age 14 to 16Challenge Level

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

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