Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples

Multiplication Squares

Age 7 to 11Challenge Level

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 Moons of Vuvv

Age 7 to 11Challenge Level

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Gran, How Old Are You?

Age 7 to 11Challenge Level

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Three Dice

Age 7 to 11Challenge Level

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Ip Dip

Age 5 to 11Challenge Level

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Surprising Split

Age 7 to 11Challenge Level

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Curious Number

Age 7 to 11Challenge Level

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Times Tables Shifts

Age 7 to 11Challenge Level

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Sets of Numbers

Age 7 to 11Challenge Level

How many different sets of numbers with at least four members can you find in the numbers in this box?

Neighbours

Age 7 to 11Challenge Level

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?

Tiling

Age 7 to 11Challenge Level

An investigation that gives you the opportunity to make and justify predictions.

Round and Round the Circle

Age 7 to 11Challenge Level

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.

Crossings

Age 7 to 11Challenge Level

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Mystery Matrix

Age 7 to 11Challenge Level

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Being Collaborative - Primary Number

Age 5 to 11Challenge Level

Number problems at primary level to work on with others.

Fitted

Age 7 to 11Challenge Level

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?

Scoring with Dice

Age 7 to 11Challenge Level

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Number Tracks

Age 7 to 11Challenge Level

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Divide it Out

Age 7 to 11Challenge Level

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Ducking and Dividing

Age 7 to 11Challenge Level

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Path to the Stars

Age 7 to 11Challenge Level

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Seven Flipped

Age 7 to 11Challenge Level

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Being Resilient - Primary Number

Age 5 to 11Challenge Level

Number problems at primary level that may require resilience.

Abundant Numbers

Age 7 to 11Challenge Level

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?

Star Product Sudoku

Age 11 to 16Challenge 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.

Sweets in a Box

Age 7 to 11Challenge Level

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?

Diagonal Product Sudoku

Age 11 to 16Challenge Level

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

Sets of Four Numbers

Age 7 to 11Challenge Level

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Red Balloons, Blue Balloons

Age 7 to 11Challenge Level

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

Zios and Zepts

Age 7 to 11Challenge Level

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?

It Figures

Age 7 to 11Challenge Level

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Multiply Multiples 2

Age 7 to 11Challenge Level

Can you work out some different ways to balance this equation?

Gabriel's Problem

Age 11 to 14Challenge Level

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

Multiply Multiples 3

Age 7 to 11Challenge Level

Have a go at balancing this equation. Can you find different ways of doing it?

Multiply Multiples 1

Age 7 to 11Challenge Level

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

A Square Deal

Age 7 to 11Challenge Level

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Three Neighbours

Age 7 to 11Challenge Level

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

How Old Are the Children?

Age 11 to 14Challenge Level

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Repeaters

Age 11 to 14Challenge Level

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Got it for Two

Age 7 to 14Challenge Level

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

Dicey Array

Age 5 to 11Challenge Level

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

Always, Sometimes or Never? Number

Age 7 to 11Challenge Level

Are these statements always true, sometimes true or never true?

Pebbles

Age 7 to 11Challenge 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?

Rearranged Rectangle

Age 7 to 11Challenge Level

How many different rectangles can you make using this set of rods?

Colour Wheels

Age 7 to 11Challenge Level

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Which Is Quicker?

Age 7 to 11Challenge Level

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Factoring Factorials

Age 11 to 14Challenge Level

Find the highest power of 11 that will divide into 1000! exactly.

Multiples Sudoku

Age 11 to 14Challenge Level

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

Down to Nothing

Age 7 to 11Challenge Level

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

Multiplication Series: Number Arrays

Age 5 to 11

This article for teachers describes how number arrays can be a useful representation for many number concepts.