Zero knowledge proof of integer factorization

If I have public element $W=K^r$, and $K=v^x$ should be kept secret where $v$ is a generator in $\mathbb G$, is there a way to produce a zero knowledge proof on x and r such that $W=v^{x \cdot r}$ while committing to $x$ and $r$ individually. Thanks.

Yes, you can by using Groth-sahai proofs. You can look the table page $37$, and notice in your case, it's a multi-scalar equation with unknowns the scalar $r$, and the group element $K$. If the prover knows $x$, he can also commit $xr$, use a quadratic equation proof in $\mathbb{Z}_p$, and a linear equation with unknown $xr$ and $W, g$ in clear.