# Resources tagged with: Factors and multiples

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There are 105 NRICH Mathematical resources connected to Factors and multiples, you may find related items under Properties of Numbers.

Broad Topics > Properties of Numbers > Factors and multiples

### Robotic Rotations

##### Age 11 to 16 Challenge Level:

How did the the rotation robot make these patterns?

### Alison's Quilt

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

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

### 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.

### 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?

### Shifting Times Tables

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

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

### The Remainders Game

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

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

### 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 Puzzle

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

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

### Diagonal Product Sudoku

##### Age 11 to 16 Challenge Level:

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

### Product Sudoku

##### Age 11 to 16 Challenge Level:

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

### Cuisenaire Environment

##### Age 5 to 16 Challenge Level:

An environment which simulates working with Cuisenaire rods.

### Stars

##### Age 11 to 14 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

##### 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?

### Ben's Game

##### Age 11 to 16 Challenge Level:

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

### Take Three from Five

##### Age 14 to 16 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?

### Fac-finding

##### Age 14 to 16 Challenge Level:

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

### Remainders

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

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

### 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.

### 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.

##### Age 11 to 16 Challenge Level:

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

### Number Rules - OK

##### Age 14 to 16 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

##### 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...

### One to Eight

##### Age 11 to 14 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.

### Why 24?

##### Age 14 to 16 Challenge Level:

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

### Funny Factorisation

##### Age 11 to 16 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?

### Beelines

##### Age 14 to 16 Challenge Level:

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

### Expenses

##### Age 14 to 16 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

##### Age 7 to 14 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

##### 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.

### Summing Consecutive Numbers

##### Age 11 to 14 Challenge 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?

### Counting Factors

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

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

### Common Divisor

##### Age 14 to 16 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.

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

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

### Statement Snap

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

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

### Satisfying Statements

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

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

### Number Families

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

How many different number families can you find?

### 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?

### 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?

### 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?

### Substitution Transposed

##### Age 11 to 16 Challenge Level:

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

### Transposition Cipher

##### Age 11 to 16 Challenge Level:

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

### Sieve of Eratosthenes

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

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

### 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?

### 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?

### 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?

### Four Coloured Lights

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

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

### Drawing Celtic Knots

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

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

### Multiples Sudoku

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

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