Given $C=XF$, and only data for $C$, solving for $X$ and $F$ has been described as not tractable (which I'm content to believe, but others aren't). If that's the case, where does the following argument fall apart?
Suppose $C^i=XF^i$ is written: $\begin{bmatrix} C_1^i \\\ \vdots \\\ C_m^i \end{bmatrix} = \begin{align}\begin{bmatrix} X_{1,1} & \dots & X_{1,n} \\\ \vdots & & \vdots \\\ X_{m,1} & \dots & X_{m,n} \end{bmatrix}\end{align}\begin{bmatrix} F_1^i \\\ \vdots \\\ F_n^i \end{bmatrix}$
One instance of data for a given $i$ of $C^i$ would produce $m$ equations and $mn+n$ unknowns.
$q$ instances of data for $C^i$ would produce $qm$ equations and $mn+qn$ unknowns.
If the supposition that you need more equations than unknowns is sufficient, why can I contradict others statements of not tractability by choosing whole number values to satisfy the inequality:
$qm >= mn+qn$?
Using say $q=6,m=3,n=2$.