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#### Resources tagged with Factors and multiples similar to Magician's Hat:

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### There are 144 results

Broad Topics > Numbers and the Number System > Factors and multiples

### What Do You Need?

##### Stage: 2 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?

### Two Much

##### Stage: 3 Challenge Level:

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

### Hot Pursuit

##### Stage: 3 Challenge Level:

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

### Diggits

##### Stage: 3 Challenge Level:

Can you find what the last two digits of the number $4^{1999}$ are?

### Remainder

##### Stage: 3 Challenge Level:

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

### X Marks the Spot

##### Stage: 3 Challenge Level:

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

### Sets of Numbers

##### Stage: 2 Challenge Level:

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

### Mathematical Swimmer

##### Stage: 3 Challenge Level:

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

### Number Tracks

##### Stage: 2 Challenge 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?

### Which Is Quicker?

##### Stage: 2 Challenge Level:

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

### Eminit

##### Stage: 3 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?

### Becky's Number Plumber

##### Stage: 2 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?

### Sets of Four Numbers

##### Stage: 2 Challenge 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?

### Big Powers

##### Stage: 3 and 4 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.

### Three Neighbours

##### Stage: 2 Challenge Level:

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

### Exploring Simple Mappings

##### Stage: 3 Challenge Level:

Explore the relationship between simple linear functions and their graphs.

### Remainders

##### Stage: 3 Challenge Level:

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

### Reverse to Order

##### Stage: 3 Challenge Level:

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

### Number Detective

##### Stage: 2 Challenge Level:

Follow the clues to find the mystery number.

##### Stage: 3 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. . . .

### A Mixed-up Clock

##### Stage: 2 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

##### Stage: 2 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.

### Inclusion Exclusion

##### Stage: 3 Challenge Level:

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

### Even So

##### Stage: 3 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?

### Three Times Seven

##### Stage: 3 Challenge Level:

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

### Factor-multiple Chains

##### Stage: 2 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?

### Times Right

##### Stage: 3 and 4 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?

### AB Search

##### Stage: 3 Challenge Level:

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

### Seven Flipped

##### Stage: 2 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.

### Thirty Six Exactly

##### Stage: 3 Challenge Level:

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

### Crossings

##### Stage: 2 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?

### Curious Number

##### Stage: 2 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?

### Ip Dip

##### Stage: 1 and 2 Challenge 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 ...?

### Counting Cogs

##### Stage: 2 and 3 Challenge Level:

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

### Which Numbers? (2)

##### Stage: 2 Challenge Level:

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

### Factor Track

##### Stage: 2 and 3 Challenge Level:

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

### Sieve of Eratosthenes

##### Stage: 3 Challenge Level:

Follow this recipe for sieving numbers and see what interesting patterns emerge.

### Multiply Multiples 3

##### Stage: 2 Challenge Level:

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

### Multiply Multiples 2

##### Stage: 2 Challenge Level:

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

### Multiply Multiples 1

##### Stage: 2 Challenge Level:

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

### Which Numbers? (1)

##### Stage: 2 Challenge Level:

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

### Table Patterns Go Wild!

##### Stage: 2 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.

### Multiplication Series: Number Arrays

##### Stage: 1 and 2

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

### Factoring Factorials

##### Stage: 3 Challenge Level:

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

### Spelling Circle

##### Stage: 2 Challenge Level:

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

### Being Determined - Primary Number

##### Stage: 1 and 2 Challenge Level:

Number problems at primary level that may require determination.

### Neighbours

##### Stage: 2 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?

### Three Spinners

##### Stage: 2 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?

### Being Collaborative - Primary Number

##### Stage: 1 and 2 Challenge Level:

Number problems at primary level to work on with others.