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.

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?

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?

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

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

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?

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

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

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

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

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

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.

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

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

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

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?

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.

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

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?

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?

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

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

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

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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.

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?

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.

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

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

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.

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?"

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?

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!?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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

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?

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

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?

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 puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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

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. . . .

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

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

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

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