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Resources tagged with Factors and multiples similar to N000ughty Thoughts:

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

N000ughty Thoughts

Stage: 4 Challenge Level:

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

Mod 3

Stage: 4 Challenge Level:

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

Sixational

Stage: 4 and 5 Challenge Level:

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

For What?

Stage: 4 Challenge Level:

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

A Biggy

Stage: 4 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.

What Numbers Can We Make Now?

Stage: 3 and 4 Challenge Level:

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

Common Divisor

Stage: 4 Challenge 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.

Number Rules - OK

Stage: 4 Challenge Level:

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

Factorial

Stage: 4 Challenge Level:

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

Helen's Conjecture

Stage: 3 Challenge Level:

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

Multiplication Magic

Stage: 4 Challenge 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). . . .

Data Chunks

Stage: 4 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. . . .

LCM Sudoku

Stage: 4 Challenge Level:

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

Stage: 3 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?

Multiplication Equation Sudoku

Stage: 4 and 5 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.

Squaresearch

Stage: 4 Challenge Level:

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

Powerful Factorial

Stage: 3 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!?

Take Three from Five

Stage: 3 and 4 Challenge Level:

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Really Mr. Bond

Stage: 4 Challenge Level:

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

Factoring Factorials

Stage: 3 Challenge Level:

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

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.

LCM Sudoku II

Stage: 3, 4 and 5 Challenge Level:

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

Transposition Cipher

Stage: 3 and 4 Challenge Level:

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

Substitution Transposed

Stage: 3 and 4 Challenge Level:

Substitution and Transposition all in one! How fiendish can these codes get?

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?

Product Sudoku 2

Stage: 3 and 4 Challenge Level:

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

Factors and Multiples - Secondary Resources

Stage: 3 and 4 Challenge Level:

A collection of resources to support work on Factors and Multiples at Secondary level.

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. . . .

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?

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?

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?

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?

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?

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?

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.

Napier's Location Arithmetic

Stage: 4 Challenge Level:

Have you seen this way of doing multiplication ?

What Numbers Can We Make?

Stage: 3 Challenge Level:

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

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.

GOT IT Now

Stage: 2 and 3 Challenge Level:

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Exploring Simple Mappings

Stage: 3 Challenge Level:

Explore the relationship between simple linear functions and their graphs.

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?

What a Joke

Stage: 4 Challenge Level:

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

Product Sudoku

Stage: 3, 4 and 5 Challenge Level:

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

Different by One

Stage: 4 Challenge Level:

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

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?

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?

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" .

Ewa's Eggs

Stage: 3 Challenge Level:

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?