FTCE General Knowledge Math Practice Test

What is the result of the factorial of 0 (0!)?

1. 1

2. 0

3. Undefined

4. None of the above

The correct answer is: 1

The factorial of a number is defined as the product of all positive integers from 1 up to that number. However, the factorial of 0 is a unique case defined by convention. In combinatorial mathematics, it is established that 0! equals 1. This convention is useful in various mathematical contexts, such as in counting problems where the number of ways to arrange zero objects is defined to be one way: doing nothing. This definition is also reflected in the formula for combinations, where, for example, choosing 0 elements from a set of n elements is an operation that results in one way (the empty set). Hence, the reasoning behind stating that the factorial of zero is one maintains consistency across various mathematical principles and operations. Thus, the factorial of 0 equals 1 is an accepted standard in mathematics.