Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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!?
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?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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?
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Find the highest power of 11 that will divide into 1000! exactly.
Can you work out what size grid you need to read our secret message?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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.
Is there an efficient way to work out how many factors a large number has?
Can you find any two-digit numbers that satisfy all of these statements?
How many zeros are there at the end of the number which is the product of first hundred positive integers?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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...
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Can you make lines of Cuisenaire rods that differ by 1?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Can you find any perfect numbers? Read this article to find out more...
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Play this game and see if you can figure out the computer's chosen number.
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
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.
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.
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?
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.
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
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. . . .
Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
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?
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. . . .
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
Can you find a way to identify times tables after they have been shifted up or down?
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...
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.
Given the products of adjacent cells, can you complete this Sudoku?
Can you work out how many lengths I swim each day?