Gcd.cpp

#include <cassert>
#include <cstdint>
#include <iostream>

template <class Int>;
Int gcd(Int a, Int b) {
  assert(a > 0 && b > 0);
  
  Int current_gcd = 1;
  for (Int d = 1; d * d <= a; d++) {
    if (a % d == 0) {
      if (b % d == 0) {
        current_gcd = d;
      }
      Int big_d = a / d;
      if (b % big_d == 0) {
        return big_d;
      }
    }
  }
  return current_gcd;
}

int main(void) {
  std::int64_t a, b;
  std::cin >> a >> b;
  std::cout << gcd(a, b) << std::endl;
}

Second revision uses assumption:
min(d1,d2) <= sqrt(a); max(d1,d2) >= sqrt(a); d2 = a / d1;

Or using Euclidean:
while (a > 0 && b > 0) { if (a > b) { a %= b; } else { b %= a; } } return a == 0 ? b : a;

Or simplifying and using swap inside Euclidean while:
while (b > 0) { a %= b; std::swap(a, b); } return a;