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Resources tagged with Factors and multiples similar to The Greedy Algorithm:

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

Special Sums and Products

Age 11 to 14 Challenge Level:

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Mathematical Swimmer

Age 11 to 14 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. . . .

Age 7 to 14 Challenge Level:

I added together some of my neighbours house numbers. Can you explain the patterns I noticed?

Age 11 to 14 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?

Ben's Game

Age 11 to 14 Challenge Level:

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

What a Joke

Age 14 to 16 Challenge Level:

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

Got It

Age 7 to 14 Challenge Level:

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Really Mr. Bond

Age 14 to 16 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?

Number Rules - OK

Age 14 to 16 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...

Even So

Age 11 to 14 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

Age 11 to 14 Challenge 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...

Take Three from Five

Age 14 to 16 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?

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?

Age 11 to 14 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. . . .

Age 11 to 16 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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.

N000ughty Thoughts

Age 14 to 16 Challenge Level:

How many noughts are at the end of these giant numbers?

Counting Factors

Age 11 to 14 Challenge Level:

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

Got it for Two

Age 7 to 14 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

Common Divisor

Age 14 to 16 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.

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.

What Numbers Can We Make?

Age 11 to 14 Challenge Level:

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

Sixational

Age 14 to 18 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. . . .

Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

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?

For What?

Age 14 to 16 Challenge Level:

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

Repeaters

Age 11 to 14 Challenge 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.

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.

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?

Factor Lines

Age 7 to 14 Challenge Level:

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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.

Satisfying Statements

Age 11 to 14 Challenge Level:

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

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?

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. . . .

Robotic Rotations

Age 11 to 16 Challenge Level:

How did the the rotation robot make these patterns?

Transposition Cipher

Age 11 to 16 Challenge Level:

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

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.

Factoring Factorials

Age 11 to 14 Challenge Level:

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

Cuboids

Age 11 to 14 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Shifting Times Tables

Age 11 to 14 Challenge Level:

Can you find a way to identify times tables after they have been shifted up or down?

LCM Sudoku II

Age 11 to 18 Challenge Level:

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

Different by One

Age 14 to 16 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)

Stars

Age 11 to 14 Challenge Level:

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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 Challenge Level:

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

Helen's Conjecture

Age 11 to 14 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?

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?

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.

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.