before vowels mult-, word-forming element meaning "many, many times, much," from combining form of Latin multus "much, many," from PIE *ml-to-, from root *mel- (2) "strong, great, numerous." It was much-used in forming Latin compounds in classical times and after (such as multianimis "having much courage," multibibus "much-drinking," multicomus "having much hair," multiloquus "talkative"). Many English words that use it (multinational, etc.) are 20c. coinages.
early 15c., "commercial agent, deputy, one who buys or sells for another," from French facteur "agent, representative" (Old French factor, faitor "doer, author, creator"), from Latin factor "doer, maker, performer," in Medieval Latin, "agent," agent noun from past participle stem of facere "to do" (from PIE root *dhe- "to set, put"). In commerce, especially "a commission merchant." Mathematical sense ("The Quantities given to be multiplied one by the other are called Factors") is from 1670s. Sense of "circumstance producing a result" is attested by 1816, from the mathematical sense.
adjectival word-forming element, variant of -al (1) with connective -i-. From Latin -ialis, in which the -i- originally was from the stem of the word being attached but later came to be felt as connective.
<a href="https://www.etymonline.com/word/multifactorial">Etymology of multifactorial by etymonline</a>
Harper, D. (n.d.). Etymology of multifactorial. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/multifactorial