dF1/dy = dF2/dx : dF1/dz = dF3/dx : dF2/dz = dF3/dy
Remember that there is a vector function such that
F(x,y,z) = F1(x,y,z)i + F2(x,y,z)j + F3(x,y,z)K
Fairly simple. If you want to make a non conservative field conservative, simply add in a constant infront of your F1/F2/F3, and find the value that satisfies the above equation.