Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples

Three Dice

Age 7 to 11
Challenge Level

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

Always, Sometimes or Never? Number

Age 7 to 11
Challenge Level

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

Gabriel's Problem

Age 11 to 14
Challenge Level

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

Crossings

Age 7 to 11
Challenge 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?

Got it for Two

Age 7 to 14
Challenge Level

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

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

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

Three Neighbours

Age 7 to 11
Challenge Level

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

Repeaters

Age 11 to 14
Challenge 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.

How Old Are the Children?

Age 11 to 14
Challenge 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?"

Star Product Sudoku

Age 11 to 16
Challenge 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.

Surprising Split

Age 7 to 11
Challenge Level

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

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?

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.

Even So

Age 11 to 14
Challenge Level

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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...

Three Times Seven

Age 11 to 14
Challenge Level

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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?

A First Product Sudoku

Age 7 to 14
Challenge Level

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

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?

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?

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?

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?

Counting Factors

Age 11 to 14
Challenge Level

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

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.

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?

Three Spinners

Age 7 to 11
Challenge Level

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

Factoring Factorials

Age 11 to 14
Challenge Level

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

Ben's Game

Age 11 to 16
Challenge Level

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

Stars

Age 11 to 14
Challenge Level

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

Product Sudoku

Age 11 to 16
Challenge Level

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

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?

Tiling

Age 7 to 11
Challenge Level

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

The Remainders Game

Age 7 to 14
Challenge Level

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

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?

Exploring Simple Mappings

Age 11 to 14
Challenge Level

Explore the relationship between simple linear functions and their graphs.

Curious Number

Age 7 to 11
Challenge 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?

What Numbers Can We Make?

Age 11 to 14
Challenge Level

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

Missing Multipliers

Age 7 to 14
Challenge Level

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

What Numbers Can We Make Now?

Age 11 to 14
Challenge Level

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

Statement Snap

Age 7 to 14
Challenge Level

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

Multiples Sudoku

Age 11 to 14
Challenge Level

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

Adding All Nine

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. . . .

Hot Pursuit

Age 11 to 14
Challenge Level

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

Neighbourly Addition

Age 7 to 14
Challenge Level

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

Have You Got It?

Age 11 to 14
Challenge Level

Can you explain the strategy for winning this game with any target?

Powerful Factorial

Age 11 to 14
Challenge Level

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

Adding in Rows

Age 11 to 14
Challenge Level

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Funny Factorisation

Age 11 to 16
Challenge Level

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

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?

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.