GCD of n numbers Algorithm

The GCD (Greatest Common Divisor) of n numbers algorithm is a computational technique used to find the largest positive integer that can evenly divide all the given numbers without leaving any remainder. It is also known as the greatest common factor (GCF) or the highest common divisor (HCD). The algorithm is particularly useful in number theory, cryptography, and computer science to perform various operations, such as simplifying fractions, finding the least common multiple, and solving Diophantine equations. There are several ways to find the GCD of n numbers, but one of the most efficient and widely used methods is the Euclidean algorithm. The algorithm starts by finding the GCD of the first two numbers, then uses that result as one of the inputs to find the GCD with the next number, and so on until all numbers have been considered. The Euclidean algorithm works by iteratively applying the modulo operation, which calculates the remainder when one number is divided by another. In each iteration, the divisor becomes the new dividend, and the remainder becomes the new divisor until the remainder becomes zero, at which point the last non-zero remainder is the GCD. This process is repeated for all the given numbers, ultimately resulting in the GCD of the entire set of n numbers.
//This program aims at calculating the GCD of n numbers by division method
#include <iostream>
using namepsace std;
int main()
{
  cout << "Enter value of n:" << endl;
  cin >> n;
  int a[n];
  int i, j, gcd;
  cout << "Enter the n numbers:" << endl;
  for (i = 0; i < n; i++)
    cin >> a[i];
  j = 1; //to access all elements of the array starting from 1
  gcd = a[0];
  while (j < n)
  {
    if (a[j] % gcd == 0) //value of gcd is as needed so far
      j++;               //so we check for next element
    else
      gcd = a[j] % gcd; //calculating GCD by division method
  }
  cout << "GCD of entered n numbers:" << gcd;
}

LANGUAGE:

DARK MODE: