What Is So Special About 69! ?

A story that connects Euler’s number (e), Googol (10¹⁰⁰), and my scientific calculator!

Hemanth
Math Simplified

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An image showing 69! (sixty-nine factorial)
Image created by the author

69! is not something that you would encounter often in everyday life. I would guess that the typical person does not even encounter the factorial function frequently in day-to-day life, let alone 69!

However, most recently, a unique set of circumstances led me to an intriguing encounter with 69! In this essay, I share my little adventure with 69! and what I learned through the journey.

Before we get into the adventure, to make the story as accessible as possible, I’d like to quickly cover the factorial function first. If the factorial function is nothing new to you, feel free to skip this initial section.

What is a Factorial?

A factorial is a function in mathematics that is applied to non-negative integers. When this function is applied to an integer n, it results in a multiplicative series of all positive integers less than or equal to n. It is probably easier to look at a few examples:

What Is So Special About 69! ? — 3! = 3*2*1; 4! = 4*3*2*1; 5! = 5*4*3*2*1; n! = n*(n-1)*(n-2)…*1
Math illustrated by the author

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