Did you know that the number 220 has a really close friend, in fact they are really amicable? Let's see if we can work out who it is.....First, write down all the factors of 220. Now, add these factors together (except 220) to make a new number.  Done that?

Next, find all the factors of the new number and, you guessed it, add all those factors together (again, except the new number itself).  What number to you get? How about that!  Do you reckon there are any other pairs of numbers like that? If so, can you find them?

Can you find a number when subtracted from its reciprocal gives 1 - how amazing would that be? Well there is such a number, and it's golden in nature, can you work out what it is?  it's related to the next item....

What's with the golden spiral at the top of the page? Do you know the fabulous story of an extraordinary twelfth century Italian mathematician?  

Can numbers be perfect, and if so what does that mean?  First, write down the factors of the following numbers: 4, 6, 18, 25, 28 and 64.  Next, add up the factors of each number, except the number itself. What numbers do you get and how do they compare with the original numbers?  

Let's take an example, the number 18 has the following factors: 1, 2, 3, 6, 9 and 18. If we sum the factors (except 18) we get 21 (this is greater than our original number).  Repeat this for the other numbers.  What do you notice?  Some of the numbers are very special!  Also, what do you notice about how many factors each number has... are the square numbers different?

If the above intrigued you, take a look at the great content on the NRICH and "Maths is fun" sites. BBC Bitesize is good too!