Resources tagged with Factors and multiples similar to The Greedy Algorithm:
Other tags that relate to The Greedy Algorithm
Factors and multiples. Fractions. Famous mathematicians. Calculating with fractions. Generalising. Creating and manipulating expressions and formulae. Equivalent fractions, decimals and percentages. History of number systems. Continued fractions. Ratio.
Broad Topics > Numbers and the Number System > Factors and multiples
Special Sums and Products
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
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. . . .
Adding in Rows
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
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
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Can You Find a Perfect Number?
Can you find any perfect numbers? Read this article to find out more...
Really Mr. Bond
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
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...
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?
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
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
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Adding All Nine
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. . . .
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
N000ughty Thoughts
How many noughts are at the end of these giant numbers?
Counting Factors
Is there an efficient way to work out how many factors a large number has?
Common Divisor
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
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Sixational
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?
Can you explain the strategy for winning this game with any target?
What Numbers Can We Make Now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
For What?
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
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
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
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
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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
Can you find any two-digit numbers that satisfy all of these statements?
Eminit
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
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
How did the the rotation robot make these patterns?
Can you work out what size grid you need to read our secret message?
Factor Track
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
Find the highest power of 11 that will divide into 1000! exactly.
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
Can you find a way to identify times tables after they have been shifted up or down?
LCM Sudoku II
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Different by One
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
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?
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
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
Helen's Conjecture
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
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
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?
Find the number which has 8 divisors, such that the product of the divisors is 331776.