Factorial (n!) Practice Problems & Step-by-Step Multiplication Solutions
The factorial of a non-negative integer n (denoted as n!) is the product of all positive integers less than or equal to n. Master fundamental values (0! through 8!) and fast factorial quotient cancellations used in permutations and combinations.
š§ Core Problem-Solving Strategies
ā” Recursive Growth: n! = n Ć (nā1)!
To calculate 6!, multiply 6 by known 5! (6 Ć 120 = 720).
āļø Factorial Quotient Cancellation
When dividing factorials like 8! / 6!, cancel out the common 6!: (8 Ć 7 Ć 6!) / 6! = 8 Ć 7 = 56.
šÆ The Zero Factorial Rule: 0! = 1
By mathematical definition and empty set permutations, 0! is always equal to 1, exactly like 1! = 1.
ā Frequently Asked Questions
Why is 0! equal to 1 and not 0?
Because n! = (n+1)! / (n+1). Setting n = 0 gives 0! = 1! / 1 = 1. Combinatorially, there is exactly 1 way to arrange zero objects.
How fast do factorials grow?
Factorials grow faster than exponential functions. While 5! = 120, just 10! reaches 3,628,800.
Continue Learning & Practicing
Reinforce your understanding with printable worksheets, step-by-step guides, calculators, and speed games: