We present measurements of the decays B+ -> X(3872) K+ and B0 -> X(3872) K0 with X(3872) -> Jpsi pi+ pi-. The data sample used, collected with the BABAR detector at the PEP-II e+e- asymmetric-energy storage ring, corresponds to 455 x 10^6 BBbar pairs. Branching fraction measurements of BF(B+ -> X(3872) K+) x BF(X(3872) -> Jpsi pi+ pi-) = (8.4 +/- 1.5 +/- 0.7) x 10^{-6} and BF(B0 -> X(3872) K0) x BF(X(3872) -> Jpsi pi+ pi- = (3.5 +/- 1.9 +/- 0.4) x 10^{-6} are obtained. We set an upper limit on the natural width of the X(3872) of Gamma < 3.3 MeV/c^2 at the 90% confidence level.
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