Resources tagged with: Factors and multiples

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

Surprising Split

Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Zios and Zepts

Age 7 to 11 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 Resilient - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience.

Being Collaborative - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level to work on with others.

Scoring with Dice

Age 7 to 11 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?

Divide it Out

Age 7 to 11 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?

What Two ...?

Age 7 to 11 Short Challenge Level:

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

What Is Ziffle?

Age 7 to 11 Challenge Level:

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

Abundant Numbers

Age 7 to 11 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?

Ducking and Dividing

Age 7 to 11 Challenge Level:

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Tom's Number

Age 7 to 11 Challenge Level:

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

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?

American Billions

Age 11 to 14 Challenge Level:

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...

Diagonal Product Sudoku

Age 11 to 16 Challenge Level:

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

Mystery Matrix

Age 7 to 11 Challenge Level:

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

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?

Adding All Nine

Age 11 to 14 Challenge Level:

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

The Moons of Vuvv

Age 7 to 11 Challenge Level:

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

Round and Round the Circle

Age 7 to 11 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.

Factor Lines

Age 7 to 14 Challenge Level:

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

It Figures

Age 7 to 11 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?

Three Times Seven

Age 11 to 14 Challenge Level:

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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?

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?

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?

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?

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?

What Numbers Can We Make Now?

Age 11 to 14 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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?

Becky's Number Plumber

Age 7 to 11 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?

Flashing Lights

Age 7 to 11 Challenge Level:

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?

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?

Neighbours

Age 7 to 11 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?

Venn Diagrams

Age 5 to 11 Challenge Level:

How will you complete these Venn diagrams?

Making Pathways

Age 7 to 11 Challenge Level:

Can you find different ways of creating paths using these paving slabs?

Star Product Sudoku

Age 11 to 16 Challenge Level:

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Product Sudoku

Age 11 to 16 Challenge Level:

The clues for this Sudoku are the product of the numbers in adjacent squares.

Crossings

Age 7 to 11 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?

Number Tracks

Age 7 to 11 Challenge Level:

Ben’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?

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?

In the Money

Age 7 to 11 Challenge Level:

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

One to Eight

Age 11 to 14 Challenge Level:

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

Path to the Stars

Age 7 to 11 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?

Repeaters

Age 11 to 14 Challenge Level:

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.

Adding in Rows

Age 11 to 14 Challenge Level:

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?

How Old Are the Children?

Age 11 to 14 Challenge Level:

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?"

Three Spinners

Age 7 to 11 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?