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

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" .

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

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

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

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. . . .

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

Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.

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?

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?"

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

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

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

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

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

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...

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.

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

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

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?

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

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

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?

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

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...

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

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

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

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?

Can you work out what size grid you need to read our secret message?

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

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.

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

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

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

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.

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?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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

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