Using a sample of 106 million $psi(3686)$ decays, the branching fractions of $psi(3686) to gamma chi_{c0}, psi(3686) to gamma chi_{c1}$, and $psi(3686) to gamma chi_{c2}$ are measured with improved precision to be $(9.389 pm 0.014 pm 0.332),%$, $(9.905 pm 0.011 pm 0.353),% $, and $(9.621 pm 0.013 pm 0.272),% $, respectively, where the first uncertainties are statistical and the second ones are systematic. The product branching fractions of $psi(3686) to gamma chi_{c1}, chi_{c1} to gamma J/psi$ and $psi(3686) to gamma chi_{c2}, chi_{c2} to gamma J/psi$ and the branching fractions of $chi_{c1} to gamma J/psi$ and $chi_{c2} to gamma J/psi$ are also presented.
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