diff --git a/C++/Algorithms/RecursionAlgorithms/ExtendedEuclid'sGCD.cpp b/C++/Algorithms/RecursionAlgorithms/ExtendedEuclid'sGCD.cpp
new file mode 100644
index 00000000..fba79eea
--- /dev/null
+++ b/C++/Algorithms/RecursionAlgorithms/ExtendedEuclid'sGCD.cpp
@@ -0,0 +1,32 @@
+/*Extended Euclid's GCD
+
+An algorithm to compute integers x and y such that
+ax + by = gcd(a,b) for given a and b.
+*/
+
+#include <iostream>
+using namespace std;
+int gcd(int a, int b, int &x, int &y)
+{
+    if (a == 0)
+    {
+        x = 0;
+        y = 1;
+        return b;
+    }
+    int x1, y1;
+    int d = gcd(b % a, a, x1, y1);
+    x = y1 - (b / a) * x1;
+    y = x1;
+    return d;
+}
+
+int main()
+{
+    int x = 0, y = 0, a, b;
+    cout << "Enter two numbers: ";
+    cin >> a >> b;
+    cout << "GCD of " << a << " and " << b << ": ";
+    cout << gcd(a, b, x, y);
+    return 0;
+}
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