General fact: 8640 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Mathematical fact: 8640 is an unremarkable number.
Trivia: 8640 is an uninteresting number.
Historical date: August 27th is the day in 1921 that the British install the son of Sharif Hussein bin Ali (leader of the Arab Revolt of 1916 against the Ottoman Empire) as King Faisal I of Iraq.