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?"

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

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...

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

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

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?

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

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?

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

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?

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 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.

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

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

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?

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?

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

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?

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

Have you seen this way of doing multiplication ?

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" .

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

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

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

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

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.

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.

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

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

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?

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

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

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.

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?

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.

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

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

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?

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

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

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

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

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