What is factorial?
GeneralClass 10CBSEAnswered 25 May 2026
Answer
Factorial multiplies a positive whole number by every positive whole number below it, down to 1. Written with an exclamation mark: n!
Examples:
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- 4! = 4 × 3 × 2 × 1 = 24
- 3! = 3 × 2 × 1 = 6
- 1! = 1
- 0! = 1 (by definition a convention that makes formulas work cleanly)
Where factorials appear: whenever you count arrangements.
How many ways can 5 people stand in a line? First position: any of 5. Second: any of remaining 4. Third: any of 3. And so on: 5 × 4 × 3 × 2 × 1 = 120 = 5!
Factorials grow explosively fast:
- 10! = 3,628,800
- 20! = 2,432,902,008,176,640,000
This rapid growth is why problems involving arrangements become computationally enormous a key insight in algorithms and cryptography.
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