Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples

Cogs

Age 11 to 14
Challenge Level

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Got It

Age 7 to 14
Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Stars

Age 11 to 14
Challenge Level

Can you work out what step size to take to ensure you visit all the dots on the circle?

Have You Got It?

Age 11 to 14
Challenge Level

Can you explain the strategy for winning this game with any target?

Factors and Multiples Game

Age 7 to 16
Challenge Level

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

Factors and Multiples - Secondary Resources

Age 11 to 16
Challenge Level

A collection of resources to support work on Factors and Multiples at Secondary level.

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.

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.

Light the Lights Again

Age 7 to 11
Challenge Level

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?

Cuboids

Age 11 to 14
Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Power Crazy

Age 11 to 14
Challenge Level

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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.

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?

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?

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?

Charlie's Delightful Machine

Age 11 to 16
Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Multiplication Square Jigsaw

Age 7 to 11
Challenge Level

Can you complete this jigsaw of the multiplication square?

Special Sums and Products

Age 11 to 14
Challenge Level

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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?

Statement Snap

Age 7 to 14
Challenge Level

You'll need to know your number properties to win a game of Statement Snap...

Robotic Rotations

Age 11 to 16
Challenge Level

How did the the rotation robot make these patterns?

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?

Factors and Multiples Game for Two

Age 7 to 14
Challenge Level

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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?

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

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

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?

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?

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?

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?

Counting Factors

Age 11 to 14
Challenge Level

Is there an efficient way to work out how many factors a large number has?

Seven Flipped

Age 7 to 11
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.

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?

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...

Neighbourly Addition

Age 7 to 14
Challenge Level

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Colour Wheels

Age 7 to 11
Challenge Level

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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.

Down to Nothing

Age 7 to 11
Challenge Level

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

Can You Find a Perfect Number?

Age 7 to 14

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

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.

Mathematical Swimmer

Age 11 to 14
Challenge Level

Can you work out how many lengths I swim each day?

Counting Cogs

Age 7 to 14
Challenge Level

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

What Numbers Can We Make?

Age 11 to 14
Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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.

Sieve of Eratosthenes

Age 11 to 14
Challenge Level

Follow this recipe for sieving numbers and see what interesting patterns emerge.

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?

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?

Number Families

Age 11 to 14
Challenge Level

How many different number families can you find?

Always, Sometimes or Never? Number

Age 7 to 11
Challenge Level

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

Rearranged Rectangle

Age 7 to 11
Challenge Level

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

LCM Sudoku II

Age 11 to 18
Challenge Level

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.