# Resources tagged with: Factors and multiples

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### There are 106 results

Broad Topics > Properties of Numbers > Factors and multiples

### Factoring a Million

##### Age 14 to 16Challenge Level

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

### Fac-finding

##### Age 14 to 16Challenge Level

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

### Expenses

##### Age 14 to 16Challenge Level

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

### Flow Chart

##### Age 11 to 14Challenge Level

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

### 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?

### Remainders

##### Age 7 to 14Challenge Level

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

### AB Search

##### Age 11 to 14 ShortChallenge Level

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

### Mod 3

##### Age 14 to 16Challenge Level

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

### Divisively So

##### Age 11 to 14Challenge Level

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

### Two Much

##### Age 11 to 14Challenge Level

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

### Gaxinta

##### Age 11 to 14Challenge Level

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

### Digat

##### Age 11 to 14Challenge Level

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

### Remainder

##### Age 11 to 14Challenge Level

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

### Dozens

##### Age 7 to 14Challenge Level

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

### Squaresearch

##### Age 14 to 16Challenge Level

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

### Oh! Hidden Inside?

##### Age 11 to 14Challenge Level

Find the number which has 8 divisors, such that the product of the divisors is 331776.

### 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?

### What a Joke

##### Age 14 to 16Challenge Level

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

### Different by One

##### Age 14 to 16Challenge Level

Can you make lines of Cuisenaire rods that differ by 1?

### The Remainders Game

##### Age 7 to 14Challenge Level

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

### Multiples Sudoku

##### Age 11 to 14Challenge Level

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

### Counting Factors

##### Age 11 to 14Challenge Level

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

### Factorial

##### Age 14 to 16Challenge Level

How many zeros are there at the end of the number which is the product of first hundred positive integers?

### 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?

### 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?

### 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 Biggy

##### Age 14 to 16Challenge Level

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

### Data Chunks

##### Age 14 to 16Challenge Level

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

### A First Product Sudoku

##### Age 11 to 14Challenge Level

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

### Why 24?

##### Age 14 to 16Challenge Level

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

### Alison's Quilt

##### Age 11 to 14Challenge Level

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

### 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?

### 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...

### 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...

### 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?

### Common Divisor

##### Age 14 to 16Challenge Level

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

### 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?

### Inclusion Exclusion

##### Age 11 to 14Challenge Level

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

### Satisfying Statements

##### Age 11 to 14Challenge Level

Can you find any two-digit numbers that satisfy all of these statements?

### 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.

##### 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. . . .

### Multiplication Magic

##### Age 14 to 16Challenge Level

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .

### What Numbers Can We Make?

##### Age 11 to 14Challenge Level

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

### Transposition Cipher

##### Age 11 to 16Challenge Level

Can you work out what size grid you need to read our secret message?

### Sieve of Eratosthenes

##### Age 11 to 14Challenge Level

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

### 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.

### Factor Track

##### Age 7 to 14Challenge 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.

### Funny Factorisation

##### Age 11 to 16Challenge Level

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