let the numbers be
x-1 x x+1 x+2
x(x-1)(x+1)(x+2) = 360
since the numbers are all about equal, and since 256 = 4^4, I'd say the numbers are
x^4+2x^3-x^2-2x-360 = 0
you know the roots are all factors of 360, and you'd like to try numbers near 4, some synthetic division will quickly show that the solutions are 3,4,5,6.