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

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

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?

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

A game that tests your understanding of remainders.

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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

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?

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.

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...

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

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

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?"

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

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

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

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

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

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

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

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

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

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Have you seen this way of doing multiplication ?

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

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

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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.

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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

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

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.

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?

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

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?

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.

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?

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

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

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?

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?

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

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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.

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

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .