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

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Fitted

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Tom's Number

Stage: 2 Challenge Level: Challenge Level:1

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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Neighbours

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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Mystery Matrix

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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Flashing Lights

Stage: 2 Challenge Level: Challenge Level:1

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?

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The Moons of Vuvv

Stage: 2 Challenge Level: Challenge Level:1

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Abundant Numbers

Stage: 2 Challenge Level: Challenge Level:1

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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Sets of Numbers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How many different sets of numbers with at least four members can you find in the numbers in this box?

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What's in the Box?

Stage: 2 Challenge Level: Challenge Level:1

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?

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Which Numbers? (1)

Stage: 2 Challenge Level: Challenge Level:1

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

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Seven Flipped

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Add the Weights

Stage: 2 Challenge Level: Challenge Level:1

If you have only four weights, where could you place them in order to balance this equaliser?

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Divide it Out

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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Making Shapes

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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Multiplication Series: Number Arrays

Stage: 1 and 2

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

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Multiplication Square Jigsaw

Stage: 2 Challenge Level: Challenge Level:1

Can you complete this jigsaw of the multiplication square?

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Nineteen Hexagons

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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Same Length Trains

Stage: 1 Challenge Level: Challenge Level:1

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

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A Dotty Problem

Stage: 2 Challenge Level: Challenge Level:1

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!

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Growing Garlic

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Which Numbers? (2)

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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Table Patterns Go Wild!

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Ip Dip

Stage: 1 and 2 Challenge Level: Challenge Level:1

"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 ...?

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Pebbles

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Factor Track

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level: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.

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Are You Well Balanced?

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Number Detective

Stage: 2 Challenge Level: Challenge Level:1

Follow the clues to find the mystery number.

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I Like ...

Stage: 1 Challenge Level: Challenge Level:1

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

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Factors and Multiples Game

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

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Path to the Stars

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

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Becky's Number Plumber

Stage: 2 Challenge Level: Challenge Level:1

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

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What Is Ziffle?

Stage: 2 Challenge Level: Challenge Level:1

Can you work out what a ziffle is on the planet Zargon?

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Gran, How Old Are You?

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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What Two ...?

Stage: 2 Short Challenge Level: Challenge Level:2 Challenge Level:2

56 406 is the product of two consecutive numbers. What are these two numbers?

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Multiply Multiples 2

Stage: 2 Challenge Level: Challenge Level:1

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

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Grouping Goodies

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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Light the Lights Again

Stage: 2 Challenge Level: Challenge Level:1

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?

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Multiply Multiples 1

Stage: 2 Challenge Level: Challenge Level:1

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

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Three Neighbours

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Multiply Multiples 3

Stage: 2 Challenge Level: Challenge Level:1

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

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Doubling Fives

Stage: 1 Challenge Level: Challenge Level:1

This activity focuses on doubling multiples of five.

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Can You Find a Perfect Number?

Stage: 2 and 3

Can you find any perfect numbers? Read this article to find out more...

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Money Measure

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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Share Bears

Stage: 1 Challenge Level: Challenge Level:1

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

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Lots of Lollies

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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The Set of Numbers

Stage: 1 Challenge Level: Challenge Level:1

Can you place the numbers from 1 to 10 in the grid?

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Lots of Biscuits!

Stage: 1 Challenge Level: Challenge Level:1

Help share out the biscuits the children have made.

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Sorting Numbers

Stage: 1 Challenge Level: Challenge Level:1

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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Curious Number

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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Three Spinners

Stage: 2 Challenge Level: Challenge Level:1

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?