GCD of two numbers in C

In this topic, we will learn about GCD and find out different ways to get GCD of two numbers in C programming languages.

The GCD is a mathematical term for the Greatest Common Divisor of two or more numbers. It is the Greatest common divisor that completely divides two or more numbers without leaving any remainder. Therefore, it is also known as the Highest Common Factor (HCF) of two numbers. For example, the GCD of two numbers, 20 and 28, is 4 because both 20 and 28 are completely divisible by 1, 2, 4 (the remainder is 0), and the largest positive number among the factors 1, 2, and 4 is 4. Similarly, the GCD of two numbers, 24 and 60, is 12.

GCD of two numbers using for loop

Let's consider a program to get the GCD of two numbers in C using for loop.

Gcd_for.c

#include <stdio.h>
#include <conio.h>
int main()
{
	// declare the variables
	int n1, n2, i, GCD_Num;
	printf ( " Enter any two numbers: \n ");
	scanf ( "%d %d", &n1, &n2); 
	
	// use for loop
	for( i = 1; i <= n1 && i <= n2; ++i)
	{
		if (n1 % i ==0 && n2 % i == 0)
			GCD_Num = i; /* if n1 and n2 is completely divisible by i, the divisible number will be the GCD_Num */
	}
	// print the GCD of two numbers
	printf (" GCD of two numbers %d and %d is %d.", n1, n2, GCD_Num);
	return 0;
}

Output

Enter any two numbers:
 96
36
 GCD of two numbers 96 and 36 is 12.

GCD of two numbers using while loop

Let's consider a program to get the GCD of two numbers in C using while loop.

Gcd_while.c

#include <stdio.h>
#include <conio.h>
int main()
{	
	// initialize the local variables num1 and num2
	int num1 = 50, num2 = 60;
	
	while (num1 != num2) 
	{
		// if num1 is greater than num2, returns the num1.
		if (num1 > num2)
			{
			num1 = num1 - num2;	
			}
			// otherwise, it returns the num2.
		else
			{
				num2 = num2 - num1;
				}	
				
	} 
	// print the GCD of the number.
	printf( " GCD of two numbers 50 and 60 is %d.", num2);
}

Output

GCD of two numbers 50 and 60 is 10.

Get the GCD of N numbers from the user

Let's consider a program to get the GCD of n numbers by taking the input from the users.

gcdNum.c

#include <stdio.h>
#include <conio.h>
void main()
{
	// declaration of the variables
	int n1, n2 = -1;
	printf (" Enter N numbers from the users ( 0 to exists from the loop) \n");
	while ( 1)
	{
		scanf ( "%d", &n1); // A while loop continuously accepts the number 
		if ( n1 < 1) // n1 should be larger than 1 
			break; 
			
			
		else if ( n2 == -1) 
			n2 = n1; // assign the value of n1 to n2
		else if(n1 < n2)
			n2 = gcd_Num(n1, n2); // assign the function into the n2
		else
			n2 = gcd_Num( n2, n2); // else it stores the function value into the n2
	}
	printf (" \n GCD of all entered number is: %d", n2);
	getch();
}

// Get the GCD of two numbers
int gcd_Num ( int x, int y)
{
	int i; 
	for( i = x; i >= 1; i --)
	{	// largest number that completely divides both number
		if( x % i == 0 && y % i == 0)
			break; 
	}
	return i;	
}

Output

GCD of two numbers 50 and 60 is 10.

Get the GCD of N numbers from the user

Let's consider a program to get the GCD of n numbers by taking the input from the users.

gcdNum.c

#include <stdio.h>
#include <conio.h>
void main()
{
	// declaration of the variables
	int n1, n2 = -1;
	printf (" Enter N numbers from the users ( 0 to exists from the loop) \n");
	while ( 1)
	{
		scanf ( "%d", &n1); // A while loop continuously accepts the number 
		if ( n1 < 1) // n1 should be larger than 1 
			break; 
			
			
		else if ( n2 == -1) 
			n2 = n1; // assign the value of n1 to n2
		else if(n1 < n2)
			n2 = gcd_Num(n1, n2); // assign the function into the n2
		else
			n2 = gcd_Num( n2, n2); // else it stores the function value into the n2
	}
	printf (" \n GCD of all entered number is: %d", n2);
	getch();
}

// Get the GCD of two numbers
int gcd_Num ( int x, int y)
{
	int i; 
	for( i = x; i >= 1; i --)
	{	// largest number that completely divides both number
		if( x % i == 0 && y % i == 0)
			break; 
	}
	return i;	
}

Output

Enter the N numbers from the users ( 0 to exists from the loop)
196
224
48
96
36
256
0

 GCD of all entered number is: 4

Get the GCD of two numbers using user defined function

Let's consider a program to get the GCD of two numbers using user defined function.

Func.c

#include <stdio.h>
#include <conio.h>
GetGCD (int x, int y); 
int main()
{
	int x, y, GCD = 0;
	printf ( " Enter the first number \n ");
	scanf ("%d", &x);
	printf ( " Enter the second number \n ");
	scanf ("%d", &y); 
	GCD = GetGCD( x, y); // call the GetGCD() function in main() function
	
	// display the greatest common difference of two numbers
	printf ( " GCD of the two numbers %d and %d is %d", x, y, GCD); 
	
	getch();
}

// function definition of the GetGCD
GetGCD ( int x, int y)
{
	
	// A while loop will continue iterates till y is not equal to 0
	while (y != 0)
	{
		if ( x > y) /* if x is greater than y, the if block is executed. */
		{
			x = x - y;
		}
		else
		{
			y = y - x;
		}
	}
	return x;
}

Output

Enter the first number
96
 Enter the second number
 132
 GCD of the two numbers 96 and 132 is 12

GCD of two numbers using the modulo operator

Let's consider a program to find the GCD of two numbers using modulo operator.

Modulo.c

#include <stdio.h> #include <conio.h> void main() { // declaration of local variable int x , y; printf ( " Enter the first number: \n "); scanf (" %d", &x); printf ( " Enter the second number: \n "); scanf (" %d", &y); printf (" GCD of two number %d and %d is %d", x, y, GetGCD( x, y)); getch(); } // use a recursive function to return GCD of two numbers x and y int GetGCD (int x, int y) { if ( y == 0) // if y is equal to 0, it returns x { return x; } // use modulo operator to perform the divisibility return GetGCD (y, x % y); }

Output

Enter the first number: 256 Enter the second number: 92 GCD of two number 256 and 92 is 4

GCD of two numbers using Recursion

Let's consider a program to find the GCD of two numbers in C using Recursion.

Recursion.c

#include <stdio.h> #include <conio.h> int GCD_Rec(int num1, int num2); int main() { int num1, num2; printf( " Enter any two positive numbers \n"); scanf("%d %d", &num1, &num2); // call and print the GCD of two number using GCD_Rec() printf(" GCD of two numbers %d and %d is %d", num1, num2, GCD_Rec(num1, num2)); return 0; } int GCD_Rec(int num1, int num2) { if (num2 != 0) { return GCD_Rec( num2, num1 % num2); } else { return num1; } }

Output

Enter any two positive numbers: 60 48 GCD of two numbers 60 and 48 is 12

In the above program, the recursive function GCD_Rec() continuously calls itself until the value of num2 is equal to 0.

GCD of three numbers using if_else and for loop

Let's consider a program to get the GCD of three numbers in C using if else statement and for loop.

Gcd_num.c

#include <stdio.h> #include <conio.h> void main() { // declare the variable x, y and z. int n1, n2, n3; printf (" Enter any positive numbers: \n "); scanf ( " %d %d %d", &n1, &n2, &n3); int GCD; // use for loop to define the function and condition for ( GCD = GCD_fun( n1, n2, n3); GCD >= 1; GCD--) { if (n1 % GCD == 0 && n2 % GCD == 0 && n3 % GCD == 0) { break; } } printf (" GCD of three numbers %d, %d and %d is %d", n1, n2, n3, GCD); getch(); } int GCD_fun ( int x, int y, int z) { if ( x >= y && x >= z) { return x; } else if ( y >= x && y >= z) { return y; } else if ( z >= x && z >= y) { return z; } }

Output

Enter any positive numbers: 98 49 56 GCD of three numbers 98, 49 and 56 is 7

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GCD of two numbers in C

GCD of two numbers using for loop

GCD of two numbers using while loop

Get the GCD of N numbers from the user

Get the GCD of N numbers from the user

Get the GCD of two numbers using user defined function

GCD of two numbers using the modulo operator

GCD of two numbers using Recursion

GCD of three numbers using if_else and for loop

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