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What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these two numbers?
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Can you make square numbers by adding two prime numbers together?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
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?
Are these domino games fair? Can you explain why or why not?
Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
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.
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
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.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Can you find what the last two digits of the number $4^{1999}$ are?
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
If you have only four weights, where could you place them in order to balance this equaliser?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
An investigation that gives you the opportunity to make and justify predictions.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
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...
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?