Special Sums and Products
Age 11 to 14
Challenge Level 
The numbers 4 and 12 have a special property.
$$\begin{eqnarray} 4 + 12&= 16\\ 4 \times 12&= 48 \end{eqnarray}$$
and 16 is a factor of 48.
Find some other examples of pairs of numbers such that their sum is a factor of their product.
What condition must exist for pairs of numbers to be related in this way?
You may also like
Adding All Nine
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 other possibilities for yourself!
