We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N =4 super-Yang-Mills theory, including the nonplanar contributions. the duality completely determines the amplitudes integrand in terms of just two planar graphs. the existence of a manifestly dual gauge-theory amplitue\de trivialized the construction of the corresponding N=8 supergravity integrand, whose graph numeratiors are doubel copies (squares) of the N=4 super-Yang-Mills amplitude. We determine the amplitudes ultraviolet pole in the critical dimension of D=11/2, the same dimension as for N=4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after somplification) descirbes the ultraviolet divergence of N=8 supergravity as the subleading-in-1/N2c single-trace divergence in N=4 super-Yang-Mills theory. Show Partial Abstract