Got It game for an adult and child. How can you play so that you know you will always win?
Can you explain the strategy for winning this game with any target?
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?"
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
Given the products of adjacent cells, can you complete this Sudoku?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. 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...
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?
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?
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?
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.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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...
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.
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
Factors and Multiples game for an adult and child. How can you make sure you win this game?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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?
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.
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. . . .
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
An environment which simulates working with Cuisenaire rods.
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Can you find a way to identify times tables after they have been shifted up or down?
Play this game and see if you can figure out the computer's chosen number.
Can you find any perfect numbers? Read this article to find out more...
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" .
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
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?
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?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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. . . .
Find the highest power of 11 that will divide into 1000! exactly.