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

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 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...

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

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

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.

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?

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?

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?

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

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

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

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

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.

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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

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.

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

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

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

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

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

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

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

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

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

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

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

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. . . .

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 ?

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

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

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

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.

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

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

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

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.

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?

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?

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" .

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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?

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?

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