What numbers have an even amount of factors?

Answer 1

If it's just factors, then any number have an even amount of factors.

Let a be any number, a = 1 a

so a have two factors, 1 and a. Two is even.

But if the question is what number have an even amount of PRIME factors, then it is different. Because if a is not prime, the might exist another two numbers b and c != 1 such that a = b c. and also, b is not prime, b = d e

So a = bc = de c = c d e So a have three prime factors (1 is not prime for some reason)

Then this question is less trivial:

6 have only prime factor 2 and 3, 10 only have prime factor 2 and 5, they are even.

but 9 only have prime factor 3, so it's not an even amount, so 9 is not.