Java 程序求两个数的 GCD 或 HCF

原文:https://www . geesforgeks . org/Java-program-to-find-gcd-or-hcf-of-two-numbers/

GCD(即最大公约数)或 HCF(即最高公因数)是可以将两个给定数字相除的最大数字。

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示例:

HCF of 10 and 20 is 10, and HCF of 9 and 21 is 3.

因此，首先找出两个指定数字的所有质因数，然后找出两个给定数字中存在的所有质因数的交集。最后，返回相交元素的乘积。

注意: 两个规定数字的 GCD 如果从大的数字中减去小的数字不会改变。

例 1:

Java 语言(一种计算机语言，尤用于创建网站)

// Java program to find GCD of two numbers
class GFG {
    // Gcd of x and y using recursive function
    static int GCD(int x, int y)
    {
        // Everything is divisible by 0
        if (x == 0)
            return y;
        if (y == 0)
            return x;

        // Both the numbers are equal
        if (x == y)
            return x;

        // x is greater
        if (x > y)
            return GCD(x - y, y);
        return GCD(x, y - x);
    }

    // The Driver method
    public static void main(String[] args)
    {
        int x = 100, y = 88;
        System.out.println("GCD of " + x + " and " + y
                           + " is " + GCD(x, y));
    }
}

Output

GCD of 100 and 88 is 4

同样，你可以找到任意两个给定数字的 GCD 或 HCF。

一个有效的解决方案是利用欧几里德算法中的模算子，这是应用于本主题的最重要的算法。

例 2:

Java 语言(一种计算机语言，尤用于创建网站)

// Java program to find GCD of two 
// numbers using Euclidean algorithm
class geeksforgeeks {
    // Function to return gcd of x and y
    // recursively
    static int GCD(int x, int y)
    {
        if (y == 0)
            return x;
        return GCD(y, x % y);
    }

    // The Driver code
    public static void main(String[] args)
    {
        int x = 47, y = 91;
        System.out.println("The GCD of " + x + " and " + y
                           + " is: " + GCD(x, y));
    }
}

Output

The GCD of 47 and 91 is: 1

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