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?

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

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?"

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

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.

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?

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. . . .

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?

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.

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

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

How many zeros are there at the end of the number which is the product of first hundred positive integers?

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

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.

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

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

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

Have you seen this way of doing multiplication ?

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

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

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

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

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

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

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

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...

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?

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

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

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

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

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.

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

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

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

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. . . .

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

Explore the relationship between simple linear functions and their graphs.

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

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

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.

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

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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?

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

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

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

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?