Other tags that relate to Pareq Exists
Constructions. Pythagoras' theorem. Creating and manipulating expressions and formulae. Circle properties and circle theorems. Generalising. Similarity and congruence. Mathematical reasoning & proof. Triangles. Regular polygons and circles. Visualising.There are 106 results
Broad Topics > Properties of Numbers > Factors and multiples
Great Granddad
Age 11 to 14
Challenge Level
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
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...
Cogs
Age 11 to 14
Challenge Level
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Take Three from Five
Age 11 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?
DOTS Division
Age 14 to 16
Challenge Level
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Counting Factors
Age 11 to 14
Challenge Level
Is there an efficient way to work out how many factors a large number has?
Hypotenuse Lattice Points
Age 14 to 16
Challenge Level
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
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?
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?
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.
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.
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?
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?
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?
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?
Gabriel's Problem
Age 11 to 14
Challenge Level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Adding in Rows
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?
Neighbourly Addition
Age 7 to 14
Challenge Level
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Summing Consecutive Numbers
Age 11 to 14
Challenge Level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
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.
Have You Got It?
Age 11 to 14
Challenge Level
Can you explain the strategy for winning this game with any target?
Beelines
Age 14 to 16
Challenge Level
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
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.
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?
Diagonal Product Sudoku
Age 11 to 16
Challenge Level
Given the products of diagonally opposite cells - can you complete this Sudoku?
Cuboids
Age 11 to 14
Challenge Level
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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. . . .
Drawing Celtic Knots
Age 11 to 14
Challenge Level
Here is a chance to create some Celtic knots and explore the mathematics behind them.
Exploring Simple Mappings
Age 11 to 14
Challenge Level
Explore the relationship between simple linear functions and their graphs.
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?
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.
How Old Are the Children?
Age 11 to 14
Challenge Level
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
Alison's Quilt
Age 11 to 14
Challenge Level
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
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.
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 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.
Multiplication Magic
Age 14 to 16
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). . . .
Adding All Nine
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. . . .
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?
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?
Satisfying Statements
Age 11 to 14
Challenge Level
Can you find any two-digit numbers that satisfy all of these statements?
N000ughty Thoughts
Age 14 to 16
Challenge Level
How many noughts are at the end of these giant numbers?
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?
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.
Statement Snap
Age 7 to 14
Challenge Level
You'll need to know your number properties to win a game of Statement Snap...
NRICH is part of the family of activities in the Millennium Mathematics Project.