Resources tagged with: Factors and multiples

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There are 156 results

Broad Topics > Properties of Numbers > Factors and multiples

Scoring with Dice

Age 7 to 11
Challenge 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?

Divide it Out

Age 7 to 11
Challenge Level

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

A Mixed-up Clock

Age 7 to 11
Challenge Level

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?

Odds and Threes

Age 7 to 11
Challenge Level

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Multiplication Squares

Age 7 to 11
Challenge 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.

Abundant Numbers

Age 7 to 11
Challenge 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?

Ducking and Dividing

Age 7 to 11
Challenge 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?

The Moons of Vuvv

Age 7 to 11
Challenge Level

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

Dicey Array

Age 5 to 11
Challenge Level

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

Number Tracks

Age 7 to 11
Challenge Level

Ben’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?

What Is Ziffle?

Age 7 to 11
Challenge Level

Can you work out what a ziffle is on the planet Zargon?

Zios and Zepts

Age 7 to 11
Challenge 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?

Mystery Matrix

Age 7 to 11
Challenge Level

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

Making Pathways

Age 7 to 11
Challenge Level

Can you find different ways of creating paths using these paving slabs?

Being Resilient - Primary Number

Age 5 to 11
Challenge Level

Number problems at primary level that may require resilience.

Being Collaborative - Primary Number

Age 5 to 11
Challenge Level

Number problems at primary level to work on with others.

What Two ...?

Age 7 to 11 Short
Challenge Level

56 406 is the product of two consecutive numbers. What are these two numbers?

Which Is Quicker?

Age 7 to 11
Challenge Level

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

Fitted

Age 7 to 11
Challenge 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?

It Figures

Age 7 to 11
Challenge 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?

Two Primes Make One Square

Age 7 to 11
Challenge Level

Can you make square numbers by adding two prime numbers together?

A First Product Sudoku

Age 7 to 14
Challenge Level

Given the products of adjacent cells, can you complete this Sudoku?

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...

Multiply Multiples 1

Age 7 to 11
Challenge Level

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

Multiply Multiples 2

Age 7 to 11
Challenge Level

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

Multiply Multiples 3

Age 7 to 11
Challenge Level

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

Fractions in a Box

Age 7 to 11
Challenge Level

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.

Multiples Sudoku

Age 11 to 14
Challenge Level

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

Tom's Number

Age 7 to 11
Challenge Level

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

The Remainders Game

Age 7 to 14
Challenge Level

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

Product Sudoku

Age 11 to 16
Challenge Level

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

Number Detective

Age 5 to 11
Challenge Level

Follow the clues to find the mystery number.

Times Right

Age 11 to 16
Challenge Level

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Just Repeat

Age 11 to 14
Challenge Level

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

Factor-multiple Chains

Age 7 to 11
Challenge Level

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Seven Flipped

Age 7 to 11
Challenge 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.

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

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

Gran, How Old Are You?

Age 7 to 11
Challenge 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?

What Do You Need?

Age 7 to 11
Challenge Level

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?

Shopping Basket

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?

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.

Eminit

Age 11 to 14
Challenge Level

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Thirty Six Exactly

Age 11 to 14
Challenge Level

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Table Patterns Go Wild!

Age 7 to 11
Challenge Level

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Down to Nothing

Age 7 to 11
Challenge 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.

Times Tables Shifts

Age 7 to 11
Challenge Level

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

Neighbours

Age 7 to 11
Challenge 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?

Money Measure

Age 7 to 11
Challenge Level

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Factoring Factorials

Age 11 to 14
Challenge Level

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

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.