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 game that tests your understanding of remainders.
A game in which players take it in turns to choose a number. Can you block your opponent?
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
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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. . . .
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.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Can you find a way to identify times tables after they have been shifted up?
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?"
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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. . . .
What is the smallest number with exactly 14 divisors?
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?
Have you seen this way of doing multiplication ?
A collection of resources to support work on Factors and Multiples at Secondary level.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
For this challenge, you'll need to play Got It! 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?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Given the products of adjacent cells, can you complete this Sudoku?
Can you find any perfect numbers? Read this article to find out more...
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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. . . .
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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.
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. . . .
Find the highest power of 11 that will divide into 1000! exactly.
Can you work out what size grid you need to read our secret message?
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.
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?