Here is a quote from the cuemath website reguardinng the history of factorials:
"In the year 1677, Fabian Stedman, a British author, defined factorial as an equivalent of change ringing. Change ringing was a part of the musical performance where the musicians would ring multiple tuned bells. And it was in the year 1808, when a mathematician from France, Christian Kramp, came up with the symbol for factorial: n!. The study of factorials is at the root of several topics in mathematics, such as the number theory, algebra, geometry, probability, statistics, graph theory, and discrete mathematics, etc."