# Find two numbers whose sum and GCD are given

Given sum and gcd of two numbers and . The task is to find both the numbers a and b. If the numbers do not exist then print .

Examples:

Input: sum = 6, gcd = 2
Output: a = 4, b = 2
4 + 2 = 6 and GCD(4, 2) = 2

Input: sum = 7, gcd = 2
Output: -1
There are no such numbers whose sum is 7 and GCD is 2

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: As GCD is given then it is known that both the numbers will be multiples of it.

• Choose the first number as gcd then the other number will be sum – gcd.
• If the sum of both the numbers chosen in the previous step equals to sum then print both the numbers.
• Else the numbers do not exist and print -1 instead.

Below is the implementation of the above approach:

## C++

 `// C++ program to find two numbers ` `// whose sum and GCD is given ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find two numbers ` `// whose sum and gcd is given ` `void` `findTwoNumbers(``int` `sum, ``int` `gcd) ` `{ ` `    ``// sum != gcd checks that both the ` `    ``// numbers are positive or not ` `    ``if` `(__gcd(gcd, sum - gcd) == gcd && sum != gcd) ` `        ``cout << ``"a = "` `<< min(gcd, sum - gcd) ` `             ``<< ``", b = "` `<< sum - min(gcd, sum - gcd) ` `             ``<< endl; ` `    ``else` `        ``cout << -1 << endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `sum = 8; ` `    ``int` `gcd = 2; ` ` `  `    ``findTwoNumbers(sum, gcd); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find two numbers  ` `// whose sum and GCD is given  ` `import` `java.util.*; ` `class` `Solution{ ` ` `  `//function to find gcd of two numbers ` `static` `int` `__gcd(``int` `a,``int` `b) ` `{ ` `    ``if` `(b==``0``) ``return` `a; ` `   ``return` `__gcd(b,a%b); ` `} ` `     `  `// Function to find two numbers  ` `// whose sum and gcd is given  ` `static` `void` `findTwoNumbers(``int` `sum, ``int` `gcd)  ` `{  ` `    ``// sum != gcd checks that both the  ` `    ``// numbers are positive or not  ` `    ``if` `(__gcd(gcd, sum - gcd) == gcd && sum != gcd)  ` `        ``System.out.println(  ``"a = "` `+ Math.min(gcd, sum - gcd)  ` `            ``+ ``", b = "` `+ (``int``)(sum - Math.min(gcd, sum - gcd)) );  ` `    ``else` `        ``System.out.println( -``1` `);  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main(String args[])  ` `{  ` `    ``int` `sum = ``8``;  ` `    ``int` `gcd = ``2``;  ` ` `  `    ``findTwoNumbers(sum, gcd);  ` ` `  `}  ` ` `  ` `  `} ` `//contributed by Arnab Kundu `

## Python3

 `# Python 3 program to find two numbers ` `# whose sum and GCD is given ` `from` `math ``import` `gcd as __gcd ` ` `  `# Function to find two numbers ` `# whose sum and gcd is given ` `def` `findTwoNumbers(``sum``, gcd): ` `     `  `    ``# sum != gcd checks that both the ` `    ``# numbers are positive or not ` `    ``if` `(__gcd(gcd, ``sum` `-` `gcd) ``=``=` `gcd ``and` `                          ``sum` `!``=` `gcd): ` `        ``print``(``"a ="``, ``min``(gcd, ``sum` `-` `gcd),  ` `              ``", b ="``, ``sum` `-` `min``(gcd, ``sum` `-` `gcd)) ` `    ``else``: ` `        ``print``(``-``1``) ` `         `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``sum` `=` `8` `    ``gcd ``=` `2` ` `  `    ``findTwoNumbers(``sum``, gcd) ` ` `  `# This code is contributed by ` `# Surendra_Gangwar `

## C#

 `// C# program to find two numbers  ` `// whose sum and GCD is given  ` `using` `System; ` `class` `GFG ` `{ ` ` `  `// function to find gcd of two numbers ` `static` `int` `__gcd(``int` `a, ``int` `b) ` `{ ` `    ``if` `(b == 0)  ` `        ``return` `a; ` `    ``return` `__gcd(b, a % b); ` `} ` `     `  `// Function to find two numbers  ` `// whose sum and gcd is given  ` `static` `void` `findTwoNumbers(``int` `sum, ``int` `gcd)  ` `{  ` `    ``// sum != gcd checks that both the  ` `    ``// numbers are positive or not  ` `    ``if` `(__gcd(gcd, sum - gcd) == gcd && sum != gcd)  ` `        ``Console.WriteLine(``"a = "` `+ Math.Min(gcd, sum - gcd) +  ` `            ``", b = "` `+ (``int``)(sum - Math.Min(gcd, sum - gcd)));  ` `    ``else` `        ``Console.WriteLine( -1 );  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main()  ` `{  ` `    ``int` `sum = 8;  ` `    ``int` `gcd = 2;  ` ` `  `    ``findTwoNumbers(sum, gcd);  ` `}  ` `} ` ` `  `// This code is contributed by anuj_67.. `

## PHP

 ` `

Output:

```a = 2, b = 6
```

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