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?

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

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

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.

Can you make lines of Cuisenaire rods that differ by 1?

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.

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

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...

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?

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?"

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

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

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

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.

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

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

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. . . .

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

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

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

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?

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

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.

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?

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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?

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

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

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

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

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

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Can you work out what size grid you need to read our secret message?

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

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

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

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.

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

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

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

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?

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...

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

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

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?