Factorials (!)

Learning Objectives Define a factorial and use the factorial notation (!). Calculate the value of simple factorials (e.g., 5!, 7!). Simplify expressions involving factorials (e.g., 8!/6!). Understand and apply the special case of zero factorial (0! = 1). Solve simple equations involving factorials (e.g., n!/((n-2)!) = 12). Compare the growth rate of the factorial function to linear, quadratic, and exponential functions. How many different ways can you and your 4 friends line up for a photo? 📸 The answer involves a powerful math shortcut called a factorial! In this lesson, you'll learn about factorials, a special function that represents the product of all positive integers up to a certain number. Understanding factorials is the first step into a branch of math called...

TermDefinitionExample FactorialThe factorial of a non-negative integer 'n', denoted by n!, is the product of all positive integers less than or equal to n.5! = 5 × 4 × 3 × 2 × 1 = 120 Factorial Notation (!)The exclamation mark (!) is the symbol used in mathematics to denote the factorial operation. It is placed after a non-negative integer.The expression '6!' is read as 'six factorial'. Recursive DefinitionA way of defining a function in terms of itself. For factorials, the factorial of a number is that number multiplied by the factorial of the number one less than it.n! = n × (n-1)!. For example, 7! = 7 × 6! Zero Factorial (0!)A special case defined by convention. The value of zero factorial is 1.0! = 1. This is because there is exactly one way to arrange ze...

Definition of a Factorial (for n > 0) n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1 Use this formula to calculate the factorial of any positive integer by multiplying it by every positive integer smaller than it. Recursive Formula n! = n × (n-1)! This is extremely useful for simplifying factorial expressions. It shows that any factorial can be expressed in terms of a smaller factorial. Zero Factorial Rule 0! = 1 This is a fundamental definition used as a base case in many formulas, especially in combinatorics and probability.