Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples

Multiply Multiples 2

Age 7 to 11
Challenge Level

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

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 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?

Being Resilient - Primary Number

Age 5 to 11
Challenge Level

Number problems at primary level that may require resilience.

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?

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?

Growing Garlic

Age 5 to 11
Challenge Level

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Tiling

Age 7 to 11
Challenge Level

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

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?

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?

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?

Sweets in a Box

Age 7 to 11
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?

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?

Multiplication Squares

Age 7 to 11
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.

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?

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?

A Square Deal

Age 7 to 11
Challenge Level

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

Rearranged Rectangle

Age 7 to 11
Challenge Level

How many different rectangles can you make using this set of rods?

Number Detective

Age 5 to 11
Challenge Level

Follow the clues to find the mystery number.

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?

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.

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.

A First Product Sudoku

Age 7 to 14
Challenge Level

Given the products of adjacent cells, can you complete this Sudoku?

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?

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?

Big Powers

Age 11 to 16
Challenge Level

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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?

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?

Hot Pursuit

Age 11 to 14
Challenge Level

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

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...

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?

Even So

Age 11 to 14
Challenge Level

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

Eminit

Age 11 to 14
Challenge 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?

Thirty Six Exactly

Age 11 to 14
Challenge Level

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Multiplication Square Jigsaw

Age 7 to 11
Challenge Level

Can you complete this jigsaw of the multiplication square?

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?

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?

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?

Gran, How Old Are You?

Age 7 to 11
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?

Always, Sometimes or Never? Number

Age 7 to 11
Challenge Level

Are these statements always true, sometimes true or never true?

Gabriel's Problem

Age 11 to 14
Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Give Me Four Clues

Age 7 to 11
Challenge Level

There are eight clues to help you find the mystery number on the grid. Four of them are helpful but the other four aren't! Can you sort out the clues and find the number?

Multiples Sudoku

Age 11 to 14
Challenge Level

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Got it for Two

Age 7 to 14
Challenge Level

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

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?

Playing with Factors and Multiples

Age 5 to 11

This article for primary teachers outlines why developing an intuitive 'feel' for numbers matters, and how our activities focusing on factors and multiples can help.

Dicey Array

Age 5 to 11
Challenge Level

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

Missing Multipliers

Age 7 to 14
Challenge Level

What is the smallest number of answers you need to reveal in order to work out the missing headers?

Surprising Split

Age 7 to 11
Challenge Level

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

Odds and Threes

Age 7 to 11
Challenge Level

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.