The prime factorization of $12a^2$ is $2^2\cdot3\cdot a^2$, and the prime factorization of $20ab$ is $2^2\cdot5\cdot a\times b$. The exponent of 2 is 2, the exponent of $a$ is 1, and there is no factor of b, so the greatest common factor is $2^2\cdot a=\boxed{4a}$.
