Study of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mi>K</mml:mi></mml:math>, with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

We present measurements of the decays ${B}^{+}\ensuremath{\rightarrow}X(3872){K}^{+}$ and ${B}^{0}\ensuremath{\rightarrow}X(3872){K}^{0}$ with $X(3872)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. The data sample used, collected with the BABAR detector at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ asymmetric-energy storage ring, corresponds to $455\ifmmode\times\else\texttimes\fi{}{10}^{6}B\overline{B}$ pairs. Branching fraction measurements of $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}X(3872){K}^{+})\ifmmode\times\else\texttimes\fi{}\mathcal{B}(X(3872)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(8.4\ifmmode\pm\else\textpm\fi{}1.5\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}X(3872){K}^{0})\ifmmode\times\else\texttimes\fi{}\mathcal{B}(X(3872)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(3.5\ifmmode\pm\else\textpm\fi{}1.9\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ are obtained. We set an upper limit on the natural width of the $X(3872)$ of $\ensuremath{\Gamma}&lt;3.3\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ at the 90% confidence level.

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