Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Can you find a way to identify times tables after they have been shifted up or down?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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...
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
A collection of resources to support work on Factors and Multiples at Secondary level.
Play this game and see if you can figure out the computer's chosen number.
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.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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 puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
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 three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
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?
Can you find any two-digit numbers that satisfy all of these statements?
Can you explain the strategy for winning this game with any target?
Got It game for an adult and child. How can you play so that you know you will always win?
A game in which players take it in turns to choose a number. Can you block your opponent?
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.
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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.
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?"
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?
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
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.
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
How did the the rotation robot make these patterns?
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?
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. . . .
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? 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...
Factors and Multiples game for an adult and child. How can you make sure you win this game?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
How many zeros are there at the end of the number which is the product of first hundred positive integers?