  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.
