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 game that tests your understanding of remainders.
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
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 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 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.
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
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. . . .
Can you find a way to identify times tables after they have been shifted up?
Can you work out what a ziffle is on the planet Zargon?
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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 three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Use the interactivities to complete these Venn diagrams.
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
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.
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...
Can you complete this jigsaw of the multiplication square?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
What is the smallest number with exactly 14 divisors?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
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?
A collection of resources to support work on Factors and Multiples at Secondary level.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
The clues for this Sudoku are the product of the numbers in adjacent squares.
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
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?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Got It game for an adult and child. How can you play so that you know you will always win?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =