How to calculate the factorial of n in C language

Find the factorial of n in C language:

About To find the factorial problem of n, let’s look at a question first and use it to find the breakthrough point.

1. Problem

Problem Description

Given an integer n, find its factorial, 0≤n≤ 12

Input

Input a number n

Output

Output a number representing n Factorial

Sample Input

5

Sample Output

120

2. Analysis

Since we are looking for factorial, the breakthrough point is obvious.

The breakthrough point is : factorial

The concept and background of factorial:

1️⃣Concept:

The factorial of a positive integer (factorial ) is the product of all positive integers less than and equal to this number, and the factorial of 0 is 1. The factorial of a natural number n is written n!.

2️⃣Background:

In 1808, Christian Kramp (1760～1826) introduced this notation.

3️⃣ Calculation method of factorial:

Any natural number n greater than or equal to 1 Factorial representation method:

n!=1×2 ×3×…×(n-1)×n or n!=n×(n-1)!

Note: The factorial of 0 is 1, which is 0! =1.

1! = 1
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6
…
n! = n * (n-1) *… * 2 * 1

After understanding this, you can start to try to implement it with code, and then check the following code.

3. Solve

Regarding the factorial of n implemented in C language, at the current introductory stage, we mainly have the following two ways of writing:

First type: loop

①for loop

#include<stdio.h>int main(){
	int n;
	scanf("%d", &n);
	int fact = 1;
	int i;
	for (i = 1; i <= n; i++)
	{
		fact *= i;
	}
	printf("%d\n", fact);
	return 0;}

Test sample: 5

1 * 2 * 3 * 4 * 5 = 120

5120--------------------------------Process exited after 1.475 seconds with return value 0请按任意键继续. . .

②while loop

#include<stdio.h>int main(){
	int n;
	scanf("%d", &n);
	int fact = 1;
	int i = 1;
	while (i <= n)
	{
		fact *= i;
		i++;
	}
	printf("%d\n", fact);
	return 0;}

Test example: 6

1 * 2 * 3 * 4 * 5 * 6 = 720

6720--------------------------------Process exited after 1.549 seconds with return value 0请按任意键继续. . .

Second type: recursion (function calls itself)

1️⃣Writing method one

#include <stdio.h>int Fact(int n);int main() //主函数{
    int n, cnt;
    scanf("%d", &n);
    cnt = Fact(n);
    printf("%d\n", cnt);
    return 0;}
    int Fact(int n)    //递归函数 
    {
    int res = n;
    if (n > 1)
        res = res * Fact(n - 1);
    return res;}

Test sample: 7

7 * 6 * 5 * 4 * 3 * 2 * 1

= 1 * 2 * 3 * 4 * 5 * 6 * 7
= 5040

75040--------------------------------Process exited after 2.563 seconds with return value 0请按任意键继续. . .

Of course it can also be written like this ：

2️⃣Writing method two

#include <stdio.h>int Fact(int n) //递归函数 {
    int res = n;
    if (n > 1)
        res = res * Fact(n - 1);
    return res;}int main() //主函数 {
    int n, cnt;
    scanf("%d", &n);
    cnt = Fact(n);
    printf("%d\n", cnt);
    return 0;}

Test sample: 6

6 * 5 * 4 * 3 * 2 * 1

= 1 * 2 * 3 * 4 * 5 * 6
= 720

6720--------------------------------Process exited after 1.829 seconds with return value 0请按任意键继续. . .

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