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

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

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.

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

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

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

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

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

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

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

An environment which simulates working with Cuisenaire rods.

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?

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

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?

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.

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

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.

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.

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

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

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...

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...

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.

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.

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

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

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

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

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.

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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