c语求最大公因数的算法

以下是C语言求最大公因数的两种算法：

1.辗转相除法

#include <stdio.h>

int gcd(int a, int b) {
    int temp;
    while (b != 0) {
        temp = a % b;
        a = b;
        b = temp;
    }
    return a;
}

int main() {
    int a = 12, b = 18;
    printf("The gcd of %d and %d is %d\n", a, b, gcd(a, b)); // 输出：The gcd of 12 and 18 is 6
    return 0;
}

2.质因数分解法

#include <stdio.h>

int gcd(int a, int b) {
    int i, gcd = 1;
    for (i = 2; i <= a && i <= b; i++) {
        while (a % i == 0 && b % i == 0) {
            gcd *= i;
            a /= i;
            b /= i;
        }
    }
    return gcd;
}

int main() {
    int a = 12, b = 18;
    printf("The gcd of %d and %d is %d\n", a, b, gcd(a, b)); // 输出：The gcd of 12 and 18 is 6
    return 0;
}