Other tags that relate to 2-digit Square
Generalising. Difference of two squares. Factors and multiples. Divisibility. Creating and manipulating expressions and formulae. Integers. Place value. Mathematical reasoning & proof. Addition & subtraction. Expanding and factorising quadratics.There are 106 results
Broad Topics > Properties of Numbers > Factors and multiples
Why 24?
Age 14 to 16
Challenge Level
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
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.
Phew I'm Factored
Age 14 to 16
Challenge Level
Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.
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. . . .
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). . . .
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}.
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?
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?
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?
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?
Number Rules - OK
Age 14 to 16
Challenge Level
Can you produce convincing arguments that a selection of statements about numbers are true?
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.
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.
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?
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...
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.
Alison's Quilt
Age 11 to 14
Challenge Level
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
Can You Find a Perfect Number?
Age 7 to 14
Can you find any perfect numbers? Read this article to find out more...
The Remainders Game
Age 7 to 14
Challenge Level
Play this game and see if you can figure out the computer's chosen number.
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?
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. . . .
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?
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?
Counting Factors
Age 11 to 14
Challenge Level
Is there an efficient way to work out how many factors a large number has?
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?
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?
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?
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?
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?
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...
Product Sudoku
Age 11 to 16
Challenge Level
The clues for this Sudoku are the product of the numbers in adjacent squares.
A First Product Sudoku
Age 11 to 14
Challenge Level
Given the products of adjacent cells, can you complete this Sudoku?
Divisibility Tests
Age 11 to 16
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
Factoring Factorials
Age 11 to 14
Challenge Level
Find the highest power of 11 that will divide into 1000! exactly.
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.
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.
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?
Multiples Sudoku
Age 11 to 14
Challenge Level
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
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.
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?
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?
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.
Exploring Simple Mappings
Age 11 to 14
Challenge Level
Explore the relationship between simple linear functions and their graphs.
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!?
NRICH is part of the family of activities in the Millennium Mathematics Project.