Cardinality of field

Question

If $F_1$ is field with cardinality $2^9$ and $F_2$ is a field with cardinality $2^6$ then what is the cardinality of $F_1\cap F_2$. My answer is $2^n$ such that $n|9$ and $n|6$ That gives me $n=1$ and $n=3$ .Which one is correct can somebody help