# Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples

### Flow Chart

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

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

### Fac-finding

##### Age 14 to 16 Challenge 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.

### Oh! Hidden Inside?

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

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

### Remainder

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

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

### Two Much

##### Age 11 to 14 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.

### Mod 3

##### Age 14 to 16 Challenge Level:

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

### Gaxinta

##### Age 11 to 14 Challenge 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?

### Divisively So

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

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

### Expenses

##### Age 14 to 16 Challenge Level:

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

### Dozens

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

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

### Digat

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

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

### 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?

### Squaresearch

##### Age 14 to 16 Challenge Level:

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

### Remainders

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

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

### Factorial

##### Age 14 to 16 Challenge Level:

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

### Data Chunks

##### Age 14 to 16 Challenge 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. . . .

### 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.

### Different by One

##### Age 14 to 16 Challenge Level:

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

### A First Product Sudoku

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

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

### Product Sudoku

##### Age 11 to 16 Challenge Level:

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

### Factoring Factorials

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

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

### Inclusion Exclusion

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

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

### 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?

### Counting Factors

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

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

### 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?

### The Remainders Game

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

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

### Alison's Quilt

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

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

### 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...

### 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?

### Satisfying Statements

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

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

### A Biggy

##### Age 14 to 16 Challenge 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.

### Multiples Sudoku

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

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

### Statement Snap

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

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

### Number Families

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

How many different number families can you find?

### 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?

### Transposition Cipher

##### Age 11 to 16 Challenge Level:

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

### Sieve of Eratosthenes

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

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

### Factor Track

##### Age 7 to 14 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.

### 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?

### 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?

### LCM Sudoku

##### Age 14 to 16 Challenge Level:

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

### One to Eight

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

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

### Factoring a Million

##### Age 14 to 16 Challenge Level:

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

### Counting Cogs

##### Age 7 to 14 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?

### 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!?

### 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.