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

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?

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 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.

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?

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

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.

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

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

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

A game that tests your understanding of remainders.

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.

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.

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. . . .

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?

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.

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?

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

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?

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

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

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?

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...

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 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?

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

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

Have you seen this way of doing multiplication ?

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?

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

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

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

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

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

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?

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

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

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.

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

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?

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

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

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

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

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

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

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.