If cross product value is known , then how to calculate A vector and B vector?

Question

∇H1 × ∇H2 = V and V = (σy, x(r − z), xy) .

My question : Is there any way to find out the value of ∇H1 and ∇H2 , if vector V is given?

The answer for the given V should be V = (σy, x(r − z), xy) = (0, y, z − r) × (−x, 0, σ) where ∇H1 = (0, y, z − r) and ∇H2 = (−x, 0, σ) .