“Magic” Factorials

There are many fun facts regarding the factorials. For instance:

  • 0! = 1 by convention. As weird as it may sound, this is a fact that we must remember.
  • The number of zeroes at the end of n! is roughly n/4.
  • 70! is the smallest factorial larger than a googol.
  • The sum of the reciprocals of all factorials is e.
  • Factorials can be extended to fractions, negative numbers and complex numbers by the Gamma function.

It is possible to “peel” each layer off of a factorial and create a different factorial, as shown in the neat number pattern below. A prime pattern can be found when adding and subtracting factorials. Alternating adding and subtracting factorials, as shown in the picture, yields primes numbers until you get to 9! Continue reading ““Magic” Factorials”