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 explain the strategy for winning this game with any target?

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

A game that tests your understanding of remainders.

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

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

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 diagonally opposite cells - can you complete this Sudoku?

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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.

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?

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

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?

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

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

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.

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

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

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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.

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.

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

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

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

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

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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

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

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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?

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

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?

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. . . .

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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

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

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

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?

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?

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

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.

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

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?

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

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

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?