# Resources tagged with: Factors and multiples

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### There are 156 results

Broad Topics > Properties of Numbers > Factors and multiples

### Substitution Transposed

##### Age 11 to 16Challenge Level

Substitution and Transposition all in one! How fiendish can these codes get?

### It Figures

##### Age 7 to 11Challenge 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?

### Fitted

##### Age 7 to 11Challenge 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?

### Table Patterns Go Wild!

##### Age 7 to 11Challenge 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.

### Abundant Numbers

##### Age 7 to 11Challenge 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?

### Pebbles

##### Age 7 to 11Challenge Level

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?

### Odds and Threes

##### Age 7 to 11Challenge 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.

### Number Tracks

##### Age 7 to 11Challenge 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?

### Factor-multiple Chains

##### Age 7 to 11Challenge 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?

### Two Primes Make One Square

##### Age 7 to 11Challenge Level

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

### Ducking and Dividing

##### Age 7 to 11Challenge 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?

### What Two ...?

##### Age 7 to 11 ShortChallenge Level

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

### What Is Ziffle?

##### Age 7 to 11Challenge Level

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

### Zios and Zepts

##### Age 7 to 11Challenge 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?

### Surprising Split

##### Age 7 to 11Challenge Level

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

### Path to the Stars

##### Age 7 to 11Challenge 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?

### In the Money

##### Age 7 to 11Challenge Level

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

### Sweets in a Box

##### Age 7 to 11Challenge 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?

### Tom's Number

##### Age 7 to 11Challenge Level

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

### Dicey Array

##### Age 5 to 11Challenge Level

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

### A Mixed-up Clock

##### Age 7 to 11Challenge 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?

### Ip Dip

##### Age 5 to 11Challenge 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 ...?

### Fractions in a Box

##### Age 7 to 11Challenge Level

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

### Drawing Celtic Knots

##### Age 11 to 14Challenge Level

Here is a chance to create some Celtic knots and explore the mathematics behind them.

### Seven Flipped

##### Age 7 to 11Challenge 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.

### Making Pathways

##### Age 7 to 11Challenge Level

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

### Being Collaborative - Primary Number

##### Age 5 to 11Challenge Level

Number problems at primary level to work on with others.

### Graphing Number Patterns

##### Age 7 to 11Challenge Level

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

### Being Resilient - Primary Number

##### Age 5 to 11Challenge Level

Number problems at primary level that may require resilience.

### Divide it Out

##### Age 7 to 11Challenge Level

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

##### Age 11 to 16Challenge Level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

### Scoring with Dice

##### Age 7 to 11Challenge 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?

### Summing Consecutive Numbers

##### Age 11 to 14Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

### Guess the Dominoes for Two

##### Age 7 to 11Challenge Level

Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.

### 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.

### Multiplication Square Jigsaw

##### Age 7 to 11Challenge Level

Can you complete this jigsaw of the multiplication square?

### Multiples Grid

##### Age 7 to 11Challenge 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 16Challenge 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.

### A First Product Sudoku

##### Age 7 to 14Challenge Level

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

### What Do You Need?

##### Age 7 to 11Challenge 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?

### American Billions

##### Age 11 to 14Challenge 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...

### Times Tables Shifts

##### Age 7 to 11Challenge Level

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

### The Remainders Game

##### Age 7 to 14Challenge Level

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

### Curious Number

##### Age 7 to 11Challenge 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?

### Venn Diagrams

##### Age 5 to 11Challenge Level

How will you complete these interactive Venn diagrams?

### Star Product Sudoku

##### Age 11 to 16Challenge 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.

### Tiling

##### Age 7 to 11Challenge Level

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

### Three Spinners

##### Age 7 to 11Challenge Level

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

### Product Sudoku

##### Age 11 to 16Challenge Level

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

### Crossings

##### Age 7 to 11Challenge 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?