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

### Factor Track

##### Stage: 2 and 3 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.

### Counting Cogs

##### Stage: 2 and 3 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?

### Exploring Simple Mappings

##### Stage: 3 Challenge Level:

Explore the relationship between simple linear functions and their graphs.

### Shifting Times Tables

##### Stage: 3 Challenge Level:

Can you find a way to identify times tables after they have been shifted up?

### The Remainders Game

##### Stage: 2 and 3 Challenge Level:

A game that tests your understanding of remainders.

### Napier's Location Arithmetic

##### Stage: 4 Challenge Level:

Have you seen this way of doing multiplication ?

### Factors and Multiples Game

##### Stage: 2, 3 and 4 Challenge Level:

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

### Factors and Multiples Puzzle

##### Stage: 3 Challenge Level:

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

### Substitution Cipher

##### Stage: 3 Challenge Level:

Find the frequency distribution for ordinary English, and use it to help you crack the code.

### Diagonal Product Sudoku

##### Stage: 3 and 4 Challenge Level:

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

### Product Sudoku

##### Stage: 3 Challenge Level:

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

### Stars

##### Stage: 3 Challenge Level:

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

### Cuboids

##### Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

### Ben's Game

##### Stage: 3 Challenge Level:

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

### For What?

##### Stage: 4 Challenge Level:

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

### Take Three from Five

##### Stage: 4 Challenge Level:

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

### Remainders

##### Stage: 3 Challenge Level:

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

### Got It

##### Stage: 2 and 3 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.

### Factor Lines

##### Stage: 2 and 3 Challenge Level:

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

##### Stage: 3 Challenge Level:

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

### Number Rules - OK

##### Stage: 4 Challenge Level:

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

### American Billions

##### Stage: 3 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...

### One to Eight

##### Stage: 3 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.

### Funny Factorisation

##### Stage: 3 Challenge Level:

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

### Expenses

##### Stage: 4 Challenge Level:

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

### Dozens

##### Stage: 2 and 3 Challenge Level:

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

### Big Powers

##### Stage: 3 and 4 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.

### Counting Factors

##### Stage: 3 Challenge Level:

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

### Common Divisor

##### Stage: 4 Challenge Level:

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

### Pebbles

##### Stage: 2 and 3 Challenge 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?

### Satisfying Statements

##### Stage: 3 Challenge Level:

Can you find any two-digit numbers that satisfy all of these statements?

### Gabriel's Problem

##### Stage: 3 Challenge Level:

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

### What Numbers Can We Make Now?

##### Stage: 3 Challenge Level:

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

### Substitution Transposed

##### Stage: 3 and 4 Challenge Level:

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

### Transposition Cipher

##### Stage: 3 and 4 Challenge Level:

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

### Sieve of Eratosthenes

##### Stage: 3 Challenge Level:

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

### What Numbers Can We Make?

##### Stage: 3 Challenge Level:

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

### Missing Multipliers

##### Stage: 3 Challenge Level:

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

### Charlie's Delightful Machine

##### Stage: 3 and 4 Challenge Level:

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

### LCM Sudoku II

##### Stage: 3, 4 and 5 Challenge Level:

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

### Star Product Sudoku

##### Stage: 3 and 4 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.

### Factors and Multiples - Secondary Resources

##### Stage: 3 and 4 Challenge Level:

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

### LCM Sudoku

##### Stage: 4 Challenge Level:

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

### A First Product Sudoku

##### Stage: 3 Challenge Level:

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

### There's Always One Isn't There

##### Stage: 4 Challenge Level:

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

### Data Chunks

##### Stage: 4 Challenge Level:

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

### Different by One

##### Stage: 4 Challenge Level:

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)