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

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.

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

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

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?

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

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?

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

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

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

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.

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?

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

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

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. . . .

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

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

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. . . .

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.

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

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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

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?

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

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

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?

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.

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

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

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

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

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

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.

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?

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

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?

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!?

An environment which simulates working with Cuisenaire rods.

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.

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

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

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

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 make lines of Cuisenaire rods that differ by 1?

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