Follow this recipe for sieving numbers and see what interesting patterns emerge.

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

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!?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

Find the highest power of 11 that will divide into 1000! exactly.

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.

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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?

Can you find any perfect numbers? Read this article to find out more...

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?

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?

Can you find what the last two digits of the number $4^{1999}$ are?

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

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?

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

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?

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" .

Can you find a way to identify times tables after they have been shifted up?

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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?

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. . . .

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

56 406 is the product of two consecutive numbers. What are these two numbers?

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?

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?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

A game in which players take it in turns to choose a number. Can you block your opponent?

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

A game that tests your understanding of remainders.

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?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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.

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

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. . . .

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

Explore the relationship between simple linear functions and their graphs.

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?