Teaser 2945: Infernal indices

From The Sunday Times, 3rd March 2019 [link]


The above is the size of the evil multitude in the last “Infernal indices” novel: “A deficit of daemons”.

Spoiler Alert: At the end, the forces of good engage in the fewest simultaneous battles that prevent this evil horde splitting, wholly, into equal-sized armies for that number of battles. The entire evil horde is split into one army per battle, all equally populated, bar one which has a deficit of daemons, leading to discord and a telling advantage for the forces of good.

How many battles were there?