How to Calculate Factorials

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The factorial of an integer number “n” (abbreviated as “n!”) is the product of all integer numbers that are less or equal to “n.” For example, the factorial of 4 is 24 (the product of the four numbers from 1 to 4). Factorial is not defined for negative numbers and 0!=1. Stirling's formula – n!=[sqrt(2 x pi x n)] x (n/e)^n – allows one to approximately calculate factorials given the number n is large (50 or greater). In this equation, “sqrt” is an abbreviation for the square-root operation, “pi” is 3.1416 and “e” is 2.7183. The steps below demonstrate an algorithm of the factorial calculations, using the number 5, as well as an application of the Stirling's formula.

    Write down all integer numbers from 1 to 5, separating them with the multiplication sign “x": 1 x 2 x 3 x 4 x 5.

    Perform the multiplication of the numbers in the expression from left to right. Multiply “1” and “2” to get "2." Then multiply the product “2” and "3" to get" 6." Then multiply the product “6” and “4” to get “24,” etc. Finally you would obtain 5!= 1 x 2 x 3 x 4 x 5=120.

    Calculate the factorial of 50 using Stirling's formula. 50!= [sqrt(2 x 3.1416 x 50)] x (50/2.7183)^50=sqrt(314.16)] x (18.39)^50=3.035E64. Note that this value is rounded to the thousandth; the notation “E64” means “ten in power 64.”

References

  • Excursions in Number Theory; C.S. Ogilvy; Dover Publications; Nov. 1, 1988

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