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Exponential logarithm online scientific calculator.Get Math: Factorial Definition and Factorial Formula So far we've seen a slightly looser answer to the question "What is a factorial?", but we haven't given a proper definition of factorial. Well, that's exactly what this section is for: view and explain The factorial formula and how we can find the factorial definition from it in a more mathematical way. For a more mathematical description of the factorial formula, let's look at n-factorial and how it relates to other factorials. In this case, n can be any number. If we look at the previous 5-factorial example, we can see arrive: 5!= 5 * 4!= 5 * (5-1)! If we now extrapolate it to the n factorial: n!= n * (n-1)! The above is the general factorial formula and is an integral part of the factorial definition. However, we are sure that this does not answer all the questions you may have about factorials. For example, what happens if we take a negative number? When do I Stop subtracting numbers? These are valid questions that cannot be answered by the factorial formula above, but are crucial to correctly defining factorials. These two problems can be defined by stating that the factorial formula is only defined for positive integers, which means that we cannot go below n = 1. But this also brings up another question: what is 0-factorial? Since we cannot use this formula , you'd be forgiven for thinking that the question has no answer, the whole factorial is "fake news". However, there is a "trick" to fix this: set the value of zero - by definition, the factorial to a number. And, therefore, we agreed: 0!= 1 A small disclaimer is needed here, because in mathematics things are never as simple as "pick a number and roll it", there are many complicated reasons why the value of the zero factorial is set to 1 and not anything else Numbers. However, explaining these reasons in detail is well beyond the scope of this factorial calculator.