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.
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...
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...
A collection of resources to support work on Factors and Multiples at Secondary level.
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.
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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 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?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Can you find a way to identify times tables after they have been shifted up or down?
Can you find any two-digit numbers that satisfy all of these statements?
Is there an efficient way to work out how many factors a large number has?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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 find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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?
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.
Play this game and see if you can figure out the computer's chosen number.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you work out how many lengths I swim each day?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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...
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Find the highest power of 11 that will divide into 1000! exactly.
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.
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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?
How did the the rotation robot make these patterns?
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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. . . .
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
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.
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.