How do Factotums gain spells?

[the Jester]

I'd allow it.

Again, Factotum gets a very slow spell level advancement. Dipping it does nothing other than destroy your wizard's CL. What's the fear here? Cohort (cause Leadership is totally not broken anyway)? Two PCs *gasp* working together well? I don't get it.

Speaking for my attitude, I don't think allowing it would be overpowered, but it also wouldn't fit with the way I feel the factotum does his magic in the first place. It's a flavor restriction.

I say this with my only experience of factotums being one that I played up to about 14th or 15th level; I've never dmed one.

 

[RUMBLETiGER]

Someplace said that any spell they see, they can cast so long as it's of Wizard/Sorcerer spell list, of level 7 or lower, and doesn't have an xp requirement.
Also, that they don't need a spellbook.

By RAW, it is this. The Factotum just knows all the spells he can cast at the level he can cast them.

But if true, does that mean that a Wizard level 19 with one level of Factotum who had lost all access to spells through some catastrophe could make a new spellbook on their own so long as the spells placed inside it fit the Factotum's requirements?

The answer to this is no. Because the Factotum can cast all the spells he knows at the level he knows them, The Factotum doesn't even gain the ability to access Arcane magic until level 2, a single level dip has no spells. At level 2, he only can cast 0 level spells, etc. This is without considering if a Factotum's spells would be copyable.
However, a Wizard losing his spellbook could take a Single level in Sandshaper from Sandstorm to gain 43 spells that he can immediately copy to a new spellbook.