  In this study, we compute the electromagnetic and hadronic decay widths of
the S-wave fully heavy tetraquark $T_{4Q}$ ($Q=c$ or $b$) at lowest order in
$\alpha_s$ and $v$, in the framework of nonrelativistic QCD. The short-distance
coefficients are determined through the standard procedure of matching. The
nonperturbative long-distance matrix elements are related to the
phenomenological four-body Schr\"odinger wave functions at the origin, whose
values are taken from literature. The branching fractions are predicted to be
around $10^{-3}$ and $10^{-6}$ for the $T_{4c}$ hadronic decay and
electromagnetic decay, respectively. Combing our results with the $T_{4c}$
production cross sections at the LHC, we also predict the event numbers for
various decay channels. With integrated luminosity $\mathcal{L}=100 \,{\rm
fb}^{-1}$, it is expected that the event numbers can reach $10^3- 10^4$ for
$T_{4c}\to \gamma\gamma$, and $10^5- 10^6$ for $T_{4c}\to {\rm LH}$, at the
LHC. The detecting prospect is promising.
