# Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples ### Being Resilient - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience. ### 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? ### Being Collaborative - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level to work on with others. ### 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? ### 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? ### 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. ### Two Primes Make One Square

##### Age 7 to 11 Challenge Level:

Can you make square numbers by adding two prime numbers together? ### Making Pathways

##### Age 7 to 11 Challenge Level:

Can you find different ways of creating paths using these paving slabs? ### 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? ### 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? ### What Two ...?

##### Age 7 to 11 Short Challenge Level:

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

##### Age 7 to 11 Challenge Level:

Can you work out what a ziffle is on the planet Zargon? ### 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. ### Path to the Stars

##### Age 7 to 11 Challenge 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? ### In the Money

##### Age 7 to 11 Challenge Level:

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there? ### 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? ### 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. ### 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 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? ##### Age 11 to 14 Challenge Level:

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . . ### Multiply Multiples 3

##### Age 7 to 11 Challenge Level:

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

##### Age 5 to 11 Challenge Level:

Follow the clues to find the mystery number. ### A Square Deal

##### Age 7 to 11 Challenge Level:

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65. ### 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? ### 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 Series: Number Arrays

##### Age 5 to 11

This article for teachers describes how number arrays can be a useful representation for many number concepts. ### Becky's Number Plumber

##### Age 7 to 11 Challenge Level:

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings? ### Factoring Factorials

##### Age 11 to 14 Challenge Level:

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

##### Age 7 to 11 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions. ### 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? ### Venn Diagrams

##### Age 5 to 11 Challenge Level:

How will you complete these Venn diagrams? ### 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. ### 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? ### The Remainders Game

##### Age 7 to 14 Challenge Level:

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

##### Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not? ### 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. ### 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? ### 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? ### 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... ### A First Product Sudoku

##### Age 11 to 14 Challenge Level:

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