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.
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.
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?
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 a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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.
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?
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?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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.
Given the products of adjacent cells, can you complete this Sudoku?
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.
Is there an efficient way to work out how many factors a large number has?
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 diagonally opposite cells - can you complete this Sudoku?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?"
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?
A game that tests your understanding of remainders.
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...
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?
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.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Can you find a way to identify times tables after they have been shifted up?
Have you seen this way of doing multiplication ?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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. . . .
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?
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. . . .
A game in which players take it in turns to choose a number. Can you block your opponent?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
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...
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. . . .
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
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?
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 the integer n is divisible by 4 then it can be written as the difference of two squares.
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?
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?
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
Find the number which has 8 divisors, such that the product of the divisors is 331776.