Factorial n! = n × (n-1) × (n-2) × ... × 1. Special cases: 0! = 1, 1! = 1. Properties: (n+1)! = (n+1) × n!. Applications: Counting arrangements, permutation/combination calculations. Example: 5! = 120, 4! = 24, 3! = 6. Shortcut: Simplify before calculating (e.g., 10!/8! = 10 × 9 = 90). Calculator tip: Most scientific calculators have factorial button. For large factorials, work with cancellation. Exam tip: Understand factorial represents sequential multiplication. Practice: Use in permutation/combination formulas. Know values up to 10! by memory (≈3.6 million).