Ring theory question.

Question

Why is a field with 27 elements has characteristic 3?

I was solving a question and I came to know this fact which I didn't know before.
Is there anyone who can explain this to me?
Thanks in advance.

Answer 1

Everything is well explained in Finite Field on wikipedia

All finite fields of some fixed size are unique (up to isomorphism), and any field of size $p^k$ has characteristic $p$.

Answer 2

The characteristic has to be a prime. Since the additive group has $27$ elements, it must divide $27$.

Answer 3

The characteristic of $F$ is the order of $1$ in the additive group of $F$, which is a divisor of $|F|$ per group theory and is a prime (or zero) for any field.