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 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.
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 collection of resources to support work on Factors and Multiples at Secondary level.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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...
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Play this game and see if you can figure out the computer's chosen number.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
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.
Given the products of adjacent cells, can you complete this Sudoku?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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...
Is there an efficient way to work out how many factors a large number has?
Can you find any perfect numbers? Read this article to find out more...
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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.
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?"
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Can you find a way to identify times tables after they have been shifted up or down?
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. . . .
Can you work out what size grid you need to read our secret message?
Can you find any two-digit numbers that satisfy all of these statements?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Can you make lines of Cuisenaire rods that differ by 1?
Can you work out how many lengths I swim each day?
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Find the highest power of 11 that will divide into 1000! exactly.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
How did the the rotation robot make these patterns?
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.
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?