Answer:
<em>This program is written using Java programming language</em>
import java.util.*;
public class calcGcd
{
public static void main (String [] args)
{
int num1, num2;
Scanner input = new Scanner(System.in);
//Input two integers
num1 = input.nextInt();
num2 = input.nextInt();
//Get least of the two integers
int least = num1;
if(num1 > num2)
{
least = num2;
}
//Initialize gcd to 1
int gcd = 1;
//Calculate gcd using for loop
for(int i=1;i<=least;i++)
{
if(num1%i == 0 && num2%i == 0)
{
gcd = i;
}
}
if(gcd == 1)
{
System.out.print("GCD is 1");
}
else
{
System.out.print("GCD is "+gcd);
}
}
}
Explanation:
To calculate the GCD, the program uses a for loop that iterates from 1 to the smaller number of the user input.
Within this iteration, the program checks for a common divisor of the two user inputs by the iterating element
The GCD is then displayed afterwards;
However, if the GCD is 1; the program prints the message "GCD is 1"
<em>Line by Line Explanation</em>
This line declares two integer numbers
int num1, num2;
This line allows user the program to accept user defined inputs
Scanner input = new Scanner(System.in);
The next two line allows gets inputs from the user
<em> num1 = input.nextInt();</em>
<em> num2 = input.nextInt();</em>
<em />
To calculate the GCD, the smaller of the two numbers is needed. The smaller number is derived using the following if statement
<em> int least = num1;</em>
<em> if(num1 > num2)</em>
<em> {</em>
<em> least = num2;</em>
<em> }</em>
The next line initializes GCD to 1
int gcd = 1;
The GCD is calculated using the following for loop
The GCD is the highest number that can divide both numbers
<em> for(int i=1;i<=least;i++)</em>
<em> {</em>
<em> if(num1%i == 0 && num2%i == 0)</em>
<em> {</em>
<em> gcd = i;</em>
<em> }</em>
<em> }</em>
The following is printed if the calculated GCD is 1
if(gcd == 1)
{
System.out.print("GCD is 1");
}
Otherwise, the following is printed
else
{
System.out.print("GCD is "+gcd);
}
