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

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

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?"

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.

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.

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

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

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?

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

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

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 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.

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

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?

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

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

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

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

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...

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

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

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

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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...

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

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?

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

Find the highest power of 11 that will divide into 1000! exactly.

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

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.

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

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

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

How many zeros are there at the end of the number which is the product of first hundred positive integers?

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?

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

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?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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.

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

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.

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

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