For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
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.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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.
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?
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?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Given the products of adjacent cells, can you complete this Sudoku?
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.
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?"
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.
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. . . .
A game that tests your understanding of remainders.
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?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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...
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
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" .
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A collection of resources to support work on Factors and Multiples at Secondary level.
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
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?
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?
Can you find any perfect numbers? Read this article to find out more...
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Have you seen this way of doing multiplication ?
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. . . .
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. . . .
Find the highest power of 11 that will divide into 1000! exactly.
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
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?
How many zeros are there at the end of the number which is the
product of first hundred positive integers?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
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 largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?