Greatest Common Divisor
Let a and b be integers, not both zero. The largest integer d such that d exactly divides both a and b is called the greatest common divisor of a and b . The GCD of the two integers a and b is denoted as gcd(a, b)
The Process
This implementation would follow the Euclid’s Algorithm. The gcd function for two integers is as shown below:
First we divide a with b and get the remainder r . If r is 0 then b is the GCD as it exactly divides a and obviously itself, else r might be the GCD in which case r should divide b exactly. To test for this in the next iteration the new value of a is the old value of b from the old iteration, and the new value of b is the value of r from the previous iteration. Thus the process continues while r is not 0. When r is zero that is b exactly divides a and thus b has the GCD of the initial two integers. The process to fi nd the GCD of two integers is as below:
INTEGER a, b, r;
WHILE TRUE , run loop forever
r = a%b
IF 'r' = '0'
THEN
BREAK from loop
ENDIF
a = b
b = r
ENDWHILE
Now b is the GCD of the two initial integers.
This process is used to determine the GCD of n integers. Let there be n integers 
This is implemented by taking one variable used to hold the intermediate GCD values and another the input numbers. The intermediate GCD value is set to 0, and the next input number and the current intermediate GCD result is processed and the next GCD is found. This is performed iteratively and at ith iteration.
We find the GCD of the first i integers by 
Sourcecode
#include <stdio.h>
#define TRUE 1
int gcd (int a, int b);
int
main (void)
{
int g = 0, a, i = 0;
printf ("\nFinding GCD of n integers");
printf ("\nEnter numbers serially (\"0\" to end)\n");
while (TRUE)
{
printf ("Enter Number [%d] :", i++);
scanf ("%d", &a);
/* 0 to end */
if (a == 0)
break;
/* a is used to hold the temporary value of
* * gcd at ith iteration
* */
g = gcd (g, a);
}
printf ("\nGCD is %d\n", g);
return 0;
}
int
gcd (int a, int b)
{
int rem;
if (b == 0)
return a;
while (TRUE)
{
rem = a % b;
if (rem == 0)
break;
a = b;
b = rem;
}
return b;
}
g is initialized to 0 which would be used to hold intermediate GCD results. The integers are input inside the loop and the GCD of the currently input integer a with the old value of g is found and the value of g is updated with this result which reflects the GCD of the all input integers till now. When 0 is input the loop is terminated. The function GCD is coded following the exact structure of the algorithm.
Output
Run 1: input = 35, 95, 215, 65
Finding GCD of n integers
Enter numbers serially ("0" to end )
Enter Number [1] :35
Enter Number [2] :95
Enter Number [3] :215
Enter Number [4] :65
Enter Number [5] :0
GCD is 5
Run 2: input = 221, 39, 4199, 247, 91
Finding GCD of n integers
Enter numbers serially ("0" to end )
Enter Number [1] :221
Enter Number [2] :39
Enter Number [3] :4199
Enter Number [4] :247
Enter Number [5] :91
Enter Number [6] :0
GCD is 13
Resources
Check more about GCD/HCF/GCF in wikipedia: http://en.wikipedia.org/wiki/Greatest_common_divisor
Update
27.03.2011 : Code slightly changed. gcd () function now safe from division by 0
07.05.2011 : Code updated, slight modification in iterative function.
Phoxis 