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
Follow this recipe for sieving numbers and see what interesting patterns emerge.
A game that tests your understanding of remainders.
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Given the products of adjacent cells, can you complete this Sudoku?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
What is the smallest number with exactly 14 divisors?
A collection of resources to support work on Factors and Multiples at Secondary level.
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 three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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.
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. . . .
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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 the frequency distribution for ordinary English, and use it to help you crack the code.
Can you find a way to identify times tables after they have been shifted up?
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
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 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.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
A game in which players take it in turns to choose a number. Can you block your opponent?
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Find the highest power of 11 that will divide into 1000! exactly.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
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.
Can you find any perfect numbers? Read this article to find out more...
Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .
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?
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?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
The clues for this Sudoku are the product of the numbers in adjacent squares.
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
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. . . .
Explore the relationship between simple linear functions and their
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.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?