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 diagonally opposite cells - can you complete this Sudoku?
Can you explain the strategy for winning this game with any target?
Given the products of adjacent cells, can you complete this 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.
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A game that tests your understanding of remainders.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the 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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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 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?
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 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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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?
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
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?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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...
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?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
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.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
A game in which players take it in turns to choose a number. Can you block your opponent?
Substitution and Transposition all in one! How fiendish can these codes get?
Can you work out what size grid you need to read our secret message?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Can you find any perfect numbers? Read this article to find out more...
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 frequency distribution for ordinary English, and use it to help you crack the code.
Find the highest power of 11 that will divide into 1000! exactly.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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. . . .
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?