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There are 169 NRICH Mathematical resources connected to Factors and multiples, you may find related items under Properties of numbers.
Broad Topics > Properties of numbers > Factors and multiplesEach clue in this Sudoku is the product of the two numbers in adjacent cells.
Play this game and see if you can figure out the computer's chosen number.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Can you complete this jigsaw of the multiplication square?
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
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?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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 work out what step size to take to ensure you visit all the dots on the circle?
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.
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.
Can you make square numbers by adding two prime numbers together?
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 work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
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.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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?
Can you explain the strategy for winning this game with any target?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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?