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. . . .
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.
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
Is there an efficient way to work out how many factors a large number has?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
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...
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?
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?
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?
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.
Can you find any two-digit numbers that satisfy all of these statements?
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 some of my neighbours' house numbers. Can you explain the patterns I noticed?
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?"
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
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.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
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?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
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...
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
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.
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Find the highest power of 11 that will divide into 1000! exactly.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Play this game and see if you can figure out the computer's chosen number.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Can you explain the strategy for winning this game with any target?
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. . . .
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Can you find a way to identify times tables after they have been shifted up or down?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Given the products of adjacent cells, can you complete this Sudoku?