# Resources tagged with: Factors and multiples

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### There are 154 results

Broad Topics > Properties of Numbers > Factors and multiples

### Always, Sometimes or Never? Number

##### Age 7 to 11Challenge Level

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

### What Do You Need?

##### Age 7 to 11Challenge 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?

### 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?

### 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?

### 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.

### 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?

### 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.

### Three Neighbours

##### Age 7 to 11Challenge Level

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

### 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?

### Exploring Simple Mappings

##### Age 11 to 14Challenge Level

Explore the relationship between simple linear functions and their graphs.

### Thirty Six Exactly

##### Age 11 to 14Challenge Level

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

### Eminit

##### Age 11 to 14Challenge 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?

### Even So

##### Age 11 to 14Challenge 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 14Challenge 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...

### Hot Pursuit

##### Age 11 to 14Challenge 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...

### Big Powers

##### Age 11 to 16Challenge 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.

### Just Repeat

##### Age 11 to 14Challenge 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?

### A First Product Sudoku

##### Age 11 to 14Challenge Level

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

### Odds and Threes

##### Age 7 to 11Challenge 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.

### Times Right

##### Age 11 to 16Challenge 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 14Challenge Level

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

### 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.

### A Mixed-up Clock

##### Age 7 to 11Challenge 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?

### Diagonal Product Sudoku

##### Age 11 to 16Challenge Level

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

### 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.

##### Age 11 to 14Challenge 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. . . .

### 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?

### Product Sudoku

##### Age 11 to 16Challenge Level

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

### Money Measure

##### Age 7 to 11Challenge Level

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

### 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?

### Give Me Four Clues

##### Age 7 to 11Challenge 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?

### Multiples Sudoku

##### Age 11 to 14Challenge Level

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

### 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 2

##### Age 7 to 11Challenge Level

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

### 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?

### What Numbers Can We Make Now?

##### Age 11 to 14Challenge Level

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

### Missing Multipliers

##### Age 7 to 14Challenge Level

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

### Surprising Split

##### Age 7 to 11Challenge Level

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

### Factoring Factorials

##### Age 11 to 14Challenge Level

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

### The Remainders Game

##### Age 7 to 14Challenge Level

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

### Venn Diagrams

##### Age 5 to 11Challenge Level

How will you complete these interactive Venn diagrams?

### Making Pathways

##### Age 7 to 11Challenge Level

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

### 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.

### Tiling

##### Age 7 to 11Challenge Level

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

### Three Spinners

##### Age 7 to 11Challenge Level

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

### Spelling Circle

##### Age 7 to 11Challenge Level

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

### 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?

### Three Times Seven

##### Age 11 to 14Challenge Level

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