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### A New Approach to Approximation of Factorials Using Elementary Functions Only

#### Abstract

In this paper formula for n! where n is any positive whole integer and can be as large as infinity but except 0 and 1, has been determined with error less than few in thousand. Ratio of a number n raised to the power same number n and its factorial (nn/n!) is always more than one except when the number n itself is one or zero and in those cases, ratio is one.Magnitude of this ratio depends upon the number for which factorial is to be approximated and it varies from one number to the other. Once the function that determines this ratio is ascertained, factorial of any number can be easily found out. We have derived that function called determinant function and have also eliminated the error associated with the function so derived, improved and refined it to the extent that it gives the percentage error few in thousand in approximation of factorial. We have also simplified the function so derived.In this paper of approximation of factorials, we have not used any special functions like 'O' function, error function, gamma function and have used only and only elementary functions for its easy comprehensibility to all scholars and school students alike.

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