From eba31375bd5c6407b0a1ddc41259e4aa49365884 Mon Sep 17 00:00:00 2001
From: Daredevil1343 <91751264+Daredevil1343@users.noreply.github.com>
Date: Sun, 10 Oct 2021 12:57:50 +0530
Subject: [PATCH 1/2] Added Euclidean Algorithm and it's Application.

Hi , I have added the famous Euclidean Algorithm to find GCD of numbers and also showed it's application by solving a CodeForces Division 2 (Round 81) Problem number D (Same GCDs) . Please Merge my PR under Hacktoberfest2021 tag , It'll be of huge help :)
---
 C++/Algorithm/Euclidean.cpp | 51 +++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 C++/Algorithm/Euclidean.cpp

diff --git a/C++/Algorithm/Euclidean.cpp b/C++/Algorithm/Euclidean.cpp
new file mode 100644
index 0000000..1f7912e
--- /dev/null
+++ b/C++/Algorithm/Euclidean.cpp
@@ -0,0 +1,51 @@
+/* 
+Author : Aman Agarwal
+Date : 10/10/2021
+Description : Euclidean Algorithm and It's Application.
+
+The Euclidean algorithm, discussed below,
+allows to find the greatest common divisor
+of two numbers a and b in "O(logmin(a,b))".
+The algorithm was first described in Euclid's
+"Elements" (circa 300 BC), but it is possible
+that the algorithm has even earlier origins.
+
+I used the same concept to solve CodeForces Round 81 D. Same GCDs
+Overall Time Complexity : O(sqrt(n))
+*/
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+long long n, m, t, k = 0, a, l, p;
+
+int gcd(int a, int b) {
+  if (b == 0) {
+    return a;
+  } else {
+    return gcd(b, a % b);
+  }
+}
+int main() {
+  cin >> t;
+  while (t--) {
+    cin >> a >> m;
+    n = m / gcd(a, m);
+    k = n;
+    for (long long i = 2; i * i <= n; i++) {
+      if (n % i == 0) {
+        k /= i;
+        k *= (i - 1);
+        while (n % i == 0) {
+          n /= i;
+        }
+      }
+    }
+    if (n != 1) {
+      k -= k / n;
+    }
+    cout << k << endl;
+  }
+  return 0;
+}
\ No newline at end of file

From fdac43c7fa586014c19d434b51d638b5d677845d Mon Sep 17 00:00:00 2001
From: Daredevil1343 <91751264+Daredevil1343@users.noreply.github.com>
Date: Sun, 10 Oct 2021 12:59:38 +0530
Subject: [PATCH 2/2] Update Euclidean.cpp

---
 C++/Algorithm/Euclidean.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/C++/Algorithm/Euclidean.cpp b/C++/Algorithm/Euclidean.cpp
index 1f7912e..54e5946 100644
--- a/C++/Algorithm/Euclidean.cpp
+++ b/C++/Algorithm/Euclidean.cpp
@@ -48,4 +48,4 @@ int main() {
     cout << k << endl;
   }
   return 0;
-}
\ No newline at end of file
+}