Factorial Table
Factorial & Double Factorial : āĻĢā§āĻā§āĻā§°āĻŋāĻ¯āĻŧā§āĻ˛ āĻā§°ā§ āĻĄāĻžāĻŦāĻ˛ āĻĢā§āĻā§āĻā§°āĻŋāĻ¯āĻŧā§āĻ˛
Factorial ( n! )
Definition: Factorial of a non-negative integer n is the product of all positive integers from 1 to n. āĻāĻāĻž āĻ āĻāĻŖāĻžāĻ¤ā§āĻŽāĻ āĻĒā§ā§°ā§āĻŖāĻ¸āĻāĻā§āĻ¯āĻž n ā§° āĻĢā§āĻā§āĻā§°āĻŋāĻ¯āĻŧā§āĻ˛ āĻš’āĻ˛ 1 ā§° āĻĒā§°āĻž n āĻ˛ā§ āĻ¸āĻāĻ˛ā§ āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ āĻĒā§ā§°ā§āĻŖāĻ¸āĻāĻā§āĻ¯āĻžā§° āĻā§āĻŖāĻĢāĻ˛āĨ¤
n! = n × (n-1) ×â¯× 1
Double Factorial ( n!! )
Definition: Double factorial of n is the product of numbers ≤ n that have the same parity (even or odd) as n.
n* ā§° āĻĄāĻžāĻŦāĻ˛ āĻĢā§āĻā§āĻā§°āĻŋāĻ¯āĻŧā§āĻ˛ āĻš’āĻ˛ n ā§° āĻ¸ā§āĻ¤ā§ āĻāĻā§ āĻ§ā§°āĻŖā§° (āĻā§ā§°āĻž āĻŦāĻž āĻŦāĻŋāĻā§ā§°āĻž) āĻ¸āĻāĻā§āĻ¯āĻžāĻŦā§ā§°ā§° āĻā§āĻŖāĻĢāĻ˛āĨ¤
Special Rules | āĻŦāĻŋāĻļā§āĻˇ āĻ¨āĻŋāĻ¯āĻŧāĻŽ : 0! = 1, 0!! = 1, 1!! = 1
Factorial Values
- 1! = 1
- 2! = 2
- 3! = 6
- 4! = 24
- 5! = 120
- 6! = 720
- 7! = 5,040
- 8! = 40,320
- 9! = 362,880
- 10! = 3,628,800
- 11! = 39,916,800
- 12! = 479,001,600
- 13! = 6,227,020,800
- 14! = 87,178,291,200
- 15! = 1,307,674,368,000
Double Factorial Values
Even Numbers (āĻā§ā§°āĻž āĻ¸āĻāĻā§āĻ¯āĻž)
- 2!! = 2
- 4!! = 8
- 6!! = 48
- 8!! = 384
- 10!! = 3,840
- 12!! = 46,080
- 14!! = 645,120
Odd Numbers (āĻŦāĻŋāĻā§ā§°āĻž āĻ¸āĻāĻā§āĻ¯āĻž)
- 1!! = 1
- 3!! = 3
- 5!! = 15
- 7!! = 105
- 9!! = 945
- 11!! = 10,395
- 13!! = 135,135
- 15!! = 2,027,025
Examples | āĻāĻĻāĻžāĻšā§°āĻŖ
Ex 1: Factorial
5! = 5 × 4 × 3 × 2 × 1 = 120
Ex 2: Double Factorial (Even)
8!! = 8 × 6 × 4 × 2 = 384
Ex 3: Double Factorial (Odd)
9!! = 9 × 7 × 5 × 3 × 1 = 945