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
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
A game that tests your understanding of remainders.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you find a way to identify times tables after they have been shifted up?
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. . . .
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?
Use the interactivities to complete these Venn diagrams.
Can you work out what a ziffle is on the planet Zargon?
Can you complete this jigsaw of the multiplication square?
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. . . .
Given the products of adjacent cells, can you complete this Sudoku?
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.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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.
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
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...
The clues for this Sudoku are the product of the numbers in adjacent squares.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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!
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Is there an efficient way to work out how many factors a large number has?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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.
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?
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 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?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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.