A C program to find the GCD of given numbers using recursion

By | October 2, 2013

Explanation of FUNCTION:

A function is a block of code that has a name and it has a property that it is reusable i.e. it can be executed from as many different points in a C Program as required.

Function groups a number of program statements into a unit and gives it a name. This unit can be invoked from other parts of a program. A computer program cannot handle all the tasks by itself. Instead its requests other program like entities – called functions in C – to get its tasks done. A function is a self contained block of statements that perform a coherent task of same kind.

The name of the function is unique in a C Program and is Global. It means that a function can be accessed from any location within a C Program. We pass information to the function called arguments specified when the function is called. And the function either returns some value to the point it was called from or returns nothing.

We can divide a long C program into small blocks which can perform a certain task. A function is a self contained block of statements that perform a coherent task of same kind.

 

Recursive function is a function which calls itself. Calling a function within itself makes it a endless loop. So we need to take care that there must be a termination condition in every recursive function.

For writing a function and using it in the C program, we should declare the function in the MAIN function. Declaration has to done in the area before the code starts, same area where we declare data variables.

int gcd_rec(int,int);

Function returns value and the ones which does not return any value is called and declared as void. This function which we are writing returns the gcd in decimal form as output. The values inside the round brackets are called Arguments. The Argument and return type are integer type. A function can return only one value so we have to take only one data type in which its value is expected.

Let’s identify variables needed for this program.
First variables will be the ones which will save the values entered by the user NUM1 and NUM2. Other variable will be GCD which will be for holding the resultant factorial value returned by the FUNCTION. The identified variables are GCD, NUM1, NUM2.

Now, Selection of data type is int data type due to the values expected are decimals and they will be holding smaller values so int data type is sufficient.

Main program needs only declaration of variables and function prototype. Also messages for user and scanning values  NUM1 & NUM2 and GCD is used to display the resultant values returned by the FUNCTION.

#include<stdio.h>
void main()
{
 int gcd_rec(int,int);
 int GCD,NUM1,NUM2;
 printf("\nENTER FIRST NUMBER : ");
 scanf("%d",&NUM1);
 printf("ENTER SECOND NUMBER : ");
 scanf("%d",&NUM2);
 GCD=gcd_rec(NUM1,NUM2);
 printf("\nGCD OF GIVEN NUMBERS IS %d \n",GCD);
 getch();
}

Let’s identify variables needed for function which is part of program outside main function.
Variables which are passed in the function may not be declared again which are X & YNUM1 & NUM2 are passed to the function and saved in X & Y variable of the function.

Before understanding gcd recursive function. we should now Euclid’s algorithm

euclid's gcd

Euclid’s Algorithm works on dividing first number with second number, So we have to use modulus. Now the end condition will be when one of the number becomes zero.

In this program there is a risk of generating an ENDLESS LOOP. Here we have to Check the TERMINATION condition is given or not. X & Y are values passed to the function given two numbers.  hence we should return X in if condition with Y equals zero and recursion in else condition with passing second number as first and second as the modulus of first and second numbers. In the end of the function Return X.

int gcd_rec(int X,int Y)
{
     if(Y==0)
    return(X);
    else
    gcd_rec(Y,(X%Y));
}

Note:- Remember whenever you are calling a function which is returning a value it should always be assigned to a variable of same data type or called inside the printf function as variable.

C program code :

  1. #include<stdio.h>
  2. void main()
  3. {
  4.  int gcd_rec();
  5.  int GCD,NUM1,NUM2;
  6.  printf("\nENTER FIRST NUMBER : ");
  7.  scanf("%d",&NUM1);
  8.  printf("ENTER SECOND NUMBER : ");
  9.  scanf("%d",&NUM2);
  10.  GCD=gcd_rec(NUM1,NUM2);
  11.  printf("\nGCD OF GIVEN NUMBERS IS %d \n",GCD);
  12.  getch();
  13. }
  14. int gcd_rec(int X,int Y)
  15. {
  16.  int RESULT;
  17.     if(Y==0)
  18.     return(X);
  19.     else
  20.     gcd_rec(Y,(X%Y));
  21. }

Screen Shots :-

C_program_GCD_Recursion

C_program_GCD_Recursion_Output

Leave a Reply