smc

For a positive number $n$ which is not a perfect square, exactly half of the positive factors will be less than $\sqrt{n}$. Since $60$ is not a perfect square, half of the positive factors of $60$ will be less than $\sqrt{60}\approx 7.746$. Clearly, there are no positive factors of $60$ between $7$ and $\sqrt{60}$. Therefore half of the positive factors will be less than $7$. So the answer is $\boxed{\frac{1}{2}}$.