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.

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?

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...

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.

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. . . .

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.

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?

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

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" .

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. . . .

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.

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

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

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

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...

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

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?

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

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

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

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 perfect numbers? Read this article to find out more...

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

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

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?

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.

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

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?

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.

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

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

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?

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

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

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!?

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.

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

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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

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

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

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