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.

Given the products of adjacent 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?"

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

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?

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...

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

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.

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

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.

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?

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?

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?

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

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. . . .

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.

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

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

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

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

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

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

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.

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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?

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

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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...

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

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?

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

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

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

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

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.

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?

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

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

Have you seen this way of doing multiplication ?

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

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

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?

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

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

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?