Surface Integral using divergence theorem over unit sphere?

Question

Use the Divergence Theorem to compute the surface integral $\iint_T \vec{F}^{\,}* \,d\vec{S}^{\,}$ where T is the unit sphere $x^2+y^2+z^2=1$ and $\vec{F}^{\,}$ $<x,y,z> = <y, z, x>$. I calculated the divergence of F to be 0 + 0 + 0 = 0. Does this mean that the surface integral is 0? I am confused by this result.