A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?
Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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?
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
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!?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Find the highest power of 11 that will divide into 1000! exactly.
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
How many zeros are there at the end of the number which is the product of first hundred positive integers?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
Can you find any perfect numbers? Read this article to find out more...
The clues for this Sudoku are the product of the numbers in adjacent squares.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Can you make lines of Cuisenaire rods that differ by 1?
Is there an efficient way to work out how many factors a large number has?
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. . . .
Play this game and see if you can figure out the computer's chosen number.
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
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...
Can you work out what size grid you need to read our secret message?
How many noughts are at the end of these giant numbers?
Can you find any two-digit numbers that satisfy all of these statements?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
You'll need to know your number properties to win a game of Statement Snap...
How many different number families can you find?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?