# Resources tagged with: Factors and multiples

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### There are 106 results

Broad Topics > Properties of Numbers > Factors and multiples

### Factor Lines

##### Age 7 to 14Challenge Level

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

### Factors and Multiples Game

##### Age 7 to 16Challenge Level

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

### Diagonal Product Sudoku

##### Age 11 to 16Challenge Level

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

### Got It

##### Age 7 to 14Challenge 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 14Challenge Level

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

### Cogs

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

### Have You Got It?

##### Age 11 to 14Challenge Level

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

### How Old Are the Children?

##### Age 11 to 14Challenge 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?"

### Hypotenuse Lattice Points

##### Age 14 to 16Challenge Level

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

### Gabriel's Problem

##### Age 11 to 14Challenge Level

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

### Factors and Multiples - Secondary Resources

##### Age 11 to 16Challenge Level

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

### Cuboids

##### Age 11 to 14Challenge 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?

### Factors and Multiples Game for Two

##### Age 7 to 14Challenge Level

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

### 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.

### Power Crazy

##### Age 11 to 14Challenge 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?

### Got it for Two

##### Age 7 to 14Challenge Level

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

### Sieve of Eratosthenes

##### Age 11 to 14Challenge Level

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

### Robotic Rotations

##### Age 11 to 16Challenge Level

How did the the rotation robot make these patterns?

### Beelines

##### Age 14 to 16Challenge Level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

### A First Product Sudoku

##### Age 7 to 14Challenge Level

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

### 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...

### Repeaters

##### Age 11 to 14Challenge 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.

### Multiples Sudoku

##### Age 11 to 14Challenge Level

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

### Statement Snap

##### Age 7 to 14Challenge Level

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

### Ben's Game

##### Age 11 to 16Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

### Different by One

##### Age 14 to 16Challenge Level

Can you make lines of Cuisenaire rods that differ by 1?

### The Remainders Game

##### Age 7 to 14Challenge Level

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

### Product Sudoku

##### Age 11 to 16Challenge Level

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

### Charlie's Delightful Machine

##### Age 11 to 16Challenge Level

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

### Shopping Basket

##### Age 11 to 16Challenge Level

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

### 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?

### Special Sums and Products

##### Age 11 to 14Challenge 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.

### LCM Sudoku

##### Age 14 to 16Challenge Level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

### Adding in Rows

##### Age 11 to 14Challenge 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?

### Cuisenaire Environment

##### Age 5 to 16Challenge Level

An environment which simulates working with Cuisenaire rods.

### Transposition Cipher

##### Age 11 to 16Challenge Level

Can you work out what size grid you need to read our secret message?

### 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.

### Three Times Seven

##### Age 11 to 14Challenge Level

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

### Hot Pursuit

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

### What Numbers Can We Make?

##### Age 11 to 14Challenge Level

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

### Even So

##### Age 11 to 14Challenge 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?

### Mathematical Swimmer

##### Age 11 to 14Challenge Level

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

### Eminit

##### Age 11 to 14Challenge 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 14Challenge Level

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

### Can You Find a Perfect Number?

##### Age 7 to 14

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

### Factoring Factorials

##### Age 11 to 14Challenge Level

Find the highest power of 11 that will divide into 1000! exactly.

### Drawing Celtic Knots

##### Age 11 to 14Challenge Level

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

### Number Families

##### Age 11 to 14Challenge Level

How many different number families can you find?

### Missing Multipliers

##### Age 7 to 14Challenge Level

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

### Counting Cogs

##### Age 7 to 14Challenge Level

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