I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
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.
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?
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?
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.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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.
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
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.
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Can you find any perfect numbers? Read this article to find out more...
Is there an efficient way to work out how many factors a large number has?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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. . . .
A collection of resources to support work on Factors and Multiples at Secondary level.
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.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
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 game in which players take it in turns to choose a number. Can you block your opponent?
Substitution and Transposition all in one! How fiendish can these codes get?
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?"
Can you find a way to identify times tables after they have been shifted up or down?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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?
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 did the the rotation robot make these patterns?
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...
Play this game and see if you can figure out the computer's chosen number.
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?
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?
Can you make lines of Cuisenaire rods that differ by 1?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
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. . . .
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
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?
Find the highest power of 11 that will divide into 1000! exactly.
Factors and Multiples game for an adult and child. How can you make sure you win this game?