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

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

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

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

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

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

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

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

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

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

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

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

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

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?"

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

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

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...

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

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?

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?

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

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

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?

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

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

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.

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

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

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.

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

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

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

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

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.

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" .

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!?

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

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

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

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

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

Got It game for an adult and child. How can you play so that you know you will always win?

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 is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

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.