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?
Can you explain the strategy for winning this game with any target?
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?
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 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.
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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. . . .
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 any two-digit numbers that satisfy all of these statements?
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
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. . . .
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Is there an efficient way to work out how many factors a large number has?
A collection of resources to support work on Factors and Multiples at Secondary level.
How many noughts are at the end of these giant numbers?
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?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
Have you seen this way of doing multiplication ?
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
Play this game and see if you can figure out the computer's chosen number.
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?"
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Can you find any perfect numbers? Read this article to find out more...
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?
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...
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.
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.
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
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. . . .
How did the the rotation robot make these patterns?
Can you work out what size grid you need to read our secret message?
Can you find a way to identify times tables after they have been shifted up or down?