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There are 200 NRICH Mathematical resources connected to Factors and multiples, you may find related items under Numbers and the Number System.

Broad Topics > Numbers and the Number System > Factors and multiples Robotic Rotations

Age 11 to 16 Challenge Level:

How did the the rotation robot make these patterns? Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true? Give Me Four Clues

Age 7 to 11 Challenge Level:

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? Doubling Fives

Age 5 to 7 Challenge Level:

This activity focuses on doubling multiples of five. Multiply Multiples 3

Age 7 to 11 Challenge Level:

Have a go at balancing this equation. Can you find different ways of doing it? Multiply Multiples 2

Age 7 to 11 Challenge Level:

Can you work out some different ways to balance this equation? Multiply Multiples 1

Age 7 to 11 Challenge Level:

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it? Three Neighbours

Age 7 to 11 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice? Factor Track

Age 7 to 14 Challenge Level:

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. Curious Number

Age 7 to 11 Challenge Level:

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on? Ip Dip

Age 5 to 11 Challenge Level:

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...? Light the Lights

Age 5 to 7 Challenge Level:

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights? Light the Lights Again

Age 7 to 11 Challenge Level:

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? Counting Cogs

Age 7 to 14 Challenge Level:

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why? I Like ...

Age 5 to 7 Challenge Level:

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea? Table Patterns Go Wild!

Age 7 to 11 Challenge Level:

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids. Lots of Biscuits!

Age 5 to 7 Challenge Level:

Help share out the biscuits the children have made. Times Tables Shifts

Age 7 to 11 Challenge Level:

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time? Three Dice

Age 7 to 11 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice? Shifting Times Tables

Age 11 to 14 Challenge Level:

Can you find a way to identify times tables after they have been shifted up or down? The Remainders Game

Age 7 to 14 Challenge Level:

Play this game and see if you can figure out the computer's chosen number. Venn Diagrams

Age 5 to 11 Challenge Level:

Use the interactivities to complete these Venn diagrams. What Do You Need?

Age 7 to 11 Challenge Level:

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? Growing Garlic

Age 5 to 7 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had. Factor-multiple Chains

Age 7 to 11 Challenge Level:

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers? What's in the Box?

Age 7 to 11 Challenge Level:

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? Multiplication Square Jigsaw

Age 7 to 11 Challenge Level:

Can you complete this jigsaw of the multiplication square? Music to My Ears

Age 7 to 11 Challenge Level:

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time? Clapping Times

Age 5 to 7 Challenge Level:

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud? Factors and Multiples Game

Age 7 to 16 Challenge Level:

A game in which players take it in turns to choose a number. Can you block your opponent? Factors and Multiples Puzzle

Age 11 to 14 Challenge Level:

Using your knowledge of the properties of numbers, can you fill all the squares on the board? Multiples Grid

Age 7 to 11 Challenge Level:

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? Diagonal Product Sudoku

Age 11 to 16 Challenge Level:

Given the products of diagonally opposite cells - can you complete this Sudoku? Product Sudoku

Age 11 to 14 Challenge Level:

The clues for this Sudoku are the product of the numbers in adjacent squares. Are You Well Balanced?

Age 5 to 7 Challenge Level:

Can you work out how to balance this equaliser? You can put more than one weight on a hook. Cuisenaire Environment

Age 5 to 11 Challenge Level:

An environment which simulates working with Cuisenaire rods. Same Length Trains

Age 5 to 7 Challenge Level:

How many trains can you make which are the same length as Matt's, using rods that are identical? Domino Pick

Age 5 to 7 Challenge Level:

Are these domino games fair? Can you explain why or why not? Stars

Age 11 to 14 Challenge Level:

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 hit? Cuboids

Age 11 to 14 Challenge Level:

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? Ben's Game

Age 11 to 14 Challenge Level:

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. Lots of Lollies

Age 5 to 7 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag? Share Bears

Age 5 to 7 Challenge Level:

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over? A Mixed-up Clock

Age 7 to 11 Challenge Level:

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements? For What?

Age 14 to 16 Challenge Level:

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares. Take Three from Five

Age 14 to 16 Challenge Level:

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? Fitted

Age 7 to 11 Challenge Level:

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle? Which Is Quicker?

Age 7 to 11 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why? Remainders

Age 7 to 14 Challenge Level:

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be? Telescoping Functions

Age 16 to 18

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.