FCProductSplit[exp, {v1, v2, ...}] splits expr into pieces that are free of any occurrence of v1, v2, ... and pieces that contain those variables. This works both only for products. The output is provided in the form of a two element list. One can recover the original expression by applying Times to that list.
FCProductSplit[c^2, {a}]\left\{c^2,1\right\}
FCProductSplit[a^2*b, {a}]\left\{b,a^2\right\}
FCProductSplit[(a^2 + b)*b*(c + d), {a, c}]\left\{b,\left(a^2+b\right) (c+d)\right\}