How would this have worked? If the answer was given immediately how would I validate it, even if I knew the answer in advance. I couldn't exactly remember the factors but rather some properties of them (e.g. number of digits, starting digits, ending digits).

A hallucination could just pick an arbitrary number with those same properties that I know. Maybe I could take the product of the least significant digits and see if the match or not (on the off chance the hallucination was imprecise)?