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

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.

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

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?

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 explain the strategy for winning this game with any 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?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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

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.

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

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

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

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

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...

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

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

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

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

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

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

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. . . .

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.

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

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

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

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

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

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

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

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

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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

Can you make lines of Cuisenaire rods that differ by 1?

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. . . .

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 work out how many lengths I swim each day?

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

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

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

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