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.

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

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?

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?

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

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 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?

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...

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

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?

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

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

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. . . .

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

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

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

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?"

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

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

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

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

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

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

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?

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.

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

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.

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...

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

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.

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

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?

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

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

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?

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.

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

How many noughts are at the end of these giant numbers?

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

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

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?

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

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

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

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

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.