There are **106** NRICH Mathematical resources connected to **Factors and multiples**, you may find related items under Properties of Numbers.

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

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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.

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

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Explore the relationship between simple linear functions and their graphs.

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

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

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

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

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

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

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An environment which simulates working with Cuisenaire rods.

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

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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?

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

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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?

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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.

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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 explains various divisibility rules and why they work. An article to read with pencil and paper handy.

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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.

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

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

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Can you produce convincing arguments that a selection of statements about numbers are true?

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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...

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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.

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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.

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

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

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

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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.

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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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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?

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