There were 96-gun salutes the day after her death, one for each year of her reign. Plus 21 the following day to mark the accession of King Charles.
Each of these took place in at least 5 locations - possibly more (at least one in each capital city of GB & NI, plus York that I know of).
96 gun salute in Edinburgh on arrival of the coffin there. Again in London (twice? - once at Westminster Hall, once today? - or more?)
So that's at least (96*5) + (21*5) + (96*3) = (96*8 ) + (21*5) = 768 + 105 = 873