WordReference Random House Unabridged Dictionary of American English © 2017
fac•to•ri•al  (fak tôrē əl, -tōr-),USA pronunciation n. 
  1. Mathematicsthe product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 · 3 · 2 · 1 = 24. Symbol: n!, where n is the given integer.

  1. Mathematicsof or pertaining to factors or factorials.
  2. of or pertaining to a factor or a factory.
fac•tori•al•ly, adv. 
  • factor + -ial 1810–20

Collins Concise English Dictionary © HarperCollins Publishers::

factorial /fækˈtɔːrɪəl/ n
  1. the product of all the positive integers from one up to and including a given integer. Factorial zero is assigned the value of one: factorial four is 1 × 2 × 3 × 4. Symbol: n!, where n is the given integer
  1. of or involving factorials or factors

facˈtorially adv

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