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-Euclid's Algorithm in C

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+# Euclid's Algorithm in C
+
+## Overview
+
+This C implementation calculates the Greatest Common Divisor (GCD) of two integers using Euclid's Algorithm. Euclid's Algorithm is a highly efficient method for finding the GCD, which is the largest positive integer that divides both numbers without a remainder.
+
+## Mathematical Formula
+
+Euclid's Algorithm is based on the following principle:
+
+*   GCD(a, b) = GCD(b, a mod b)  where 'a mod b' is the remainder when 'a' is divided by 'b'.
+*   GCD(a, 0) = a
+
+The algorithm repeatedly applies this formula until the second number becomes 0. At that point, the first number is the GCD.
+
+## Description of Euclid's Algorithm
+
+Euclid's Algorithm is an iterative process. Here's a breakdown:
+
+1.  **Input:** Two non-negative integers, `a` and `b`.
+2.  **Iteration:**
+    *   Calculate the remainder `r` when `a` is divided by `b` ( `r = a % b` ).
+    *   If `r` is 0, then `b` is the GCD. Return `b`.
+    *   Otherwise, set `a = b` and `b = r`.
+    *   Repeat the iteration.
+3.  **Output:** The GCD of `a` and `b`.
+
+## Uses of Euclid's Algorithm
+
+Euclid's Algorithm has numerous applications in mathematics and computer science, including:
+
+*   **Finding the Greatest Common Divisor (GCD):** The primary use, as demonstrated by this implementation.
+*   **Simplifying Fractions:** Dividing both the numerator and denominator of a fraction by their GCD reduces the fraction to its simplest form.
+*   **Cryptography:** Used in various cryptographic algorithms, such as RSA.
+*   **Modular Arithmetic:** Essential for calculations involving modular inverses and congruences.
+*   **Computer Science:** Used in hashing algorithms and other data structures.
+
+## Code Implementation
+
+The C code provides a function `euclid(int m, int b)` that implements Euclid's Algorithm iteratively.
+
+```c
+#include <stdio.h>
+#include <stdlib.h>
+
+int euclid(int m, int n) {
+  int remainder;
+
+  remainder = m % n;
+  while(remainder != 0) {
+    m = n;
+    n = remainder;
+    remainder = m % n;
+  }
+  return(n);
+}
+```
+## Usage
+
+To use the euclid function
+
+```c
+#include <stdio.h>
+
+int euclid(int m, int n); // Declare the function
+
+int main() {
+  int num1 = 48;
+  int num2 = 18;
+  int result = euclid(num1, num2);
+  printf("GCD of %d and %d is %d\n", num1, num2, result); // Output: GCD of 48 and 18 is 6
+  return 0;
+}
+```
+
+# Author
+Koree A. Smith <koree@koree.net>