Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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

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?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Can you find a way to identify times tables after they have been shifted up or down?

Given the products of diagonally opposite cells - can you complete this Sudoku?

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...

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Play this game and see if you can figure out the computer's chosen number.

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Can you explain the strategy for winning this game with any target?

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Given the products of adjacent cells, can you complete this Sudoku?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

A collection of resources to support work on Factors and Multiples at Secondary level.

Got It game for an adult and child. How can you play so that you know you will always win?

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Can you find any two-digit numbers that satisfy all of these statements?

Have you seen this way of doing multiplication ?

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

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

Can you find any perfect numbers? Read this article to find out more...

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

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

Can you find what the last two digits of the number $4^{1999}$ are?

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.