Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
A game that tests your understanding of remainders.
Can you find a way to identify times tables after they have been shifted up?
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?
Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .
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?
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.
Is there an efficient way to work out how many factors a large number has?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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 the frequency distribution for ordinary English, and use it to help you crack the code.
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.
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?
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...
Can you find any perfect numbers? Read this article to find out more...
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?"
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. . . .
Given the products of adjacent cells, can you complete this Sudoku?
Given the products of diagonally opposite cells - can you complete this Sudoku?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
Find the highest power of 11 that will divide into 1000! exactly.
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
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?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
A collection of resources to support work on Factors and Multiples at Secondary level.
Have you seen this way of doing multiplication ?
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...
Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
A game in which players take it in turns to choose a number. Can you block your opponent?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?
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.
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. . . .