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

Abundant Numbers

Stage: 2 Challenge Level:

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?

Scoring with Dice

Stage: 2 Challenge Level:

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Zios and Zepts

Stage: 2 Challenge Level:

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Being Determined - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level that may require determination.

Sets of Numbers

Stage: 2 Challenge Level:

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

Number Tracks

Stage: 2 Challenge Level:

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

A Mixed-up Clock

Stage: 2 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?

Being Collaborative - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level to work on with others.

Gran, How Old Are You?

Stage: 2 Challenge Level:

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

Ip Dip

Stage: 1 and 2 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 ...?

Round and Round the Circle

Stage: 2 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Mystery Matrix

Stage: 2 Challenge Level:

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

Got it for Two

Stage: 2 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

It Figures

Stage: 2 Challenge Level:

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

What Is Ziffle?

Stage: 2 Challenge Level:

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

Fractions in a Box

Stage: 2 Challenge Level:

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Sets of Four Numbers

Stage: 2 Challenge Level:

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

What Two ...?

Stage: 2 Short Challenge Level:

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

Two Primes Make One Square

Stage: 2 Challenge Level:

Can you make square numbers by adding two prime numbers together?

The Moons of Vuvv

Stage: 2 Challenge Level:

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

Tom's Number

Stage: 2 Challenge Level:

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

What's in the Box?

Stage: 2 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?

Divide it Out

Stage: 2 Challenge Level:

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

Multiplication Squares

Stage: 2 Challenge Level:

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Path to the Stars

Stage: 2 Challenge Level:

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?

Fitted

Stage: 2 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?

Stage: 2 Challenge Level:

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

Curious Number

Stage: 2 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?

Neighbours

Stage: 2 Challenge Level:

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?

Tiling

Stage: 2 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

Sweets in a Box

Stage: 2 Challenge Level:

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Multiply Multiples 3

Stage: 2 Challenge Level:

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

Multiply Multiples 2

Stage: 2 Challenge Level:

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

Multiply Multiples 1

Stage: 2 Challenge Level:

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

Becky's Number Plumber

Stage: 2 Challenge Level:

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?

Three Dice

Stage: 2 Challenge Level:

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

Three Neighbours

Stage: 2 Challenge Level:

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

Stage: 2 Challenge Level:

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

What Do You Need?

Stage: 2 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?

A Dotty Problem

Stage: 2 Challenge Level:

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!

Factor-multiple Chains

Stage: 2 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?

Seven Flipped

Stage: 2 Challenge Level:

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

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.

Multiples Grid

Stage: 2 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?

Crossings

Stage: 2 Challenge Level:

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Three Spinners

Stage: 2 Challenge Level:

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

Factor Lines

Stage: 2 and 3 Challenge Level:

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

A Square Deal

Stage: 2 Challenge Level:

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

In the Money

Stage: 2 Challenge Level:

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

Number Detective

Stage: 2 Challenge Level:

Follow the clues to find the mystery number.