Six is an interesting number. If you add its factors 1, 2 and 3 together, you get 6. This is a neat trick that only works for some numbers, and mathematicians describe these numbers as perfect.
The next perfect number after 6 is 28 (1 + 2 + 4 + 7 + 14 = 28), and the third perfect number is 496. But most numbers aren’t perfect. Numbers with a sum of factors that falls short of the number are known as deficient. An example is 14, where 1 + 2 + 7 = 10. Others, such as 24, have too large a sum, (1 + 2 + 3 + 4 + 6 + 8 + 12 = 36) and are called abundant.
We have found some interesting clues to help us search for perfect numbers. The Greek geometer Euclid found a way of constructing perfect even numbers. He took a type of special number called Mersenne primes and multiplied them by a certain number of 2s. Many years after Euclid, the renowned mathematician Euler showed that all perfect even numbers could be made using Euclid’s formula.