判断2个正整数是否互质

1.   Two positive integers i and j are considered to be co-prime if there exists no integer greater than 1 that divides them both. 

Write a function co-prime that has two input parameters, i and j, and returns a value of 1 for true if i and j are co-prime. 

Otherwise, co-prime should return a value of 0 for false.  Also, write a driver program to test the your function. 

You should specify the input / output format of your program.

 

使用欧几里得算法(辗转相除法)

GCD is stand for greatest common divisor最大公约数

Hint - You can use the Euclidean Algorithm which is outlined as below:

To find the greatest common divisor between two natural numbers, divide one by the other and take the remainder (i.e. modulus operation). 

为了找到2个自然数a，b的最大公约数，用一个数a除以另外一个数b，取余数

 

If the remainder is non-zero, take the divider and the modulus as the input and repeat the modulus operation until the modulus becomes zero. 

如果余数不是0，把除数和余数作为输入，重复求余的操作。直到余数变为0

 

The last divider used before the modulus becomes zero is the greatest common divisor (GCD) between the two numbers that we start out with. 

在余数变为0前的最后一个除数，是2个数字的最大公约数

 

If the GCD is 1, then the two numbers are co-prime (i.e. relatively prime).  (30 points)

如果最大公约数是1，那么这2个数字互质

Example 1: Find the GCD of 84 and 140.

140 % 84 = 56 ,  84 % 56 = 28,  56 % 28 = 0

\ the GCD of 84 and 140 is 28 Þ not co-prime.

 

Example 2: Find the GCD of 12 and 35

12 % 35 = 12,  35 % 12 = 11,  12 % 11 = 1,  11 % 1 = 0

\ the GCD of 35 and 12 is 1 Þ co-prime.

 

        public static bool CoPrime(int a,int b)
        {
            bool flag = false;
            int c;
            while (true)
            {
                c = a % b;
                if (c == 0)
                {
                    if (b == 1)
                    {
                        flag = true;
                    }
                    break;
                }
                a = b;
                b = c;
            }
            return flag;
        }

 

作者:Chuck Lu    GitHub