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- Steve Jobs

Greatest Common Divisor

What is GCD?

The Greatest Common Divisor(GCD) of two or more integers, when at least one of them is non-zero integer, is the largest positive integer that divides the numbers without any remainder.

The GCD is also well known as HCF(Highest Common Factor) or GCF(Greatest Common Factor).

GCD Examples

Two Numbers GCD Value
0, 5 5
2, 10 2
9, 12 3
24, 36, 48 12

Graphical View

When two circles of numbers 9 and 12 are joined each other then GCD of the circles are 3

greatest common divisor

When three circles of numbers 24, 36 and 48 are joind each other then GCD of the circles are 12

greatest common divisor

C Program - GCD

Let us write a simple C program to find the GCD of two integers.

c-gcd.c
#include <stdio.h>
int gcd(int num1, int num2);
int main()
{
int num1, num2;
printf("Enter two positive integers: ");
scanf("%d %d ", &num1, &num2);
printf("G.C.D of %d and %d = %d ", num1, num2, gcd(num1, num2));
return 0;
}
// Function will return gcd of two integer
int gcd(int num1, int num2)
{
if (num2 != 0)
return gcd(num2, num1%num2);
else
return num1;
}
Enter two positive integers : 0 5 
G.C.D of 0 and 5 = 5

Note:

Let us focus on int gcd() function. Here the gcd funtion of integer datatype accepts two integers as an input and returns a single integer value. if condition inside gcd function checks whether num2 is not equal to zero. i.e) if(5!=0) for us condition is true and now num1 = num2 and num2 = 0%5. Again the gcd function is called and now if condition fails as num2 = 0 and returns num1 i.e) 5

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