Given the products of diagonally opposite cells - can you complete this Sudoku?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
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.
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. . . .
A game that tests your understanding of remainders.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?"
Given the products of adjacent cells, can you complete this Sudoku?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
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
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
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?
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.
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.
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. . . .
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
A game in which players take it in turns to choose a number. Can you block your opponent?
For this challenge, you'll need to play Got It! 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.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Can you work out what size grid you need to read our secret message?
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.
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?
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...
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
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. . . .
Substitution and Transposition all in one! How fiendish can these codes get?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
How many noughts are at the end of these giant numbers?
Have you seen this way of doing multiplication ?
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 five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Can you find any perfect numbers? Read this article to find out more...
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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 zeros are there at the end of the number which is the
product of first hundred positive integers?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
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?