Solution to Euler Project Problem03 (#2069)

* Solution to Euler Project Problem03

* Solution to Euler Project Problem03
format fix

* format code

* update prime function

Co-authored-by: mickonama <mickonama@csd.auth.gr>
Co-authored-by: shellhub <shellhub.me@gmail.com>

ProjectEuler/Problem03.java

@@ -0,0 +1,62 @@
+package ProjectEuler;
+
+/**
+ * The prime factors of 13195 are 5, 7, 13 and 29.
+ *
+ * <p>What is the largest prime factor of the number 600851475143 ?
+ *
+ * <p>Link: https://projecteuler.net/problem=3
+ */
+public class Problem03 {
+
+  /**
+   * Checks if a number is prime or not
+   *
+   * @param n the number
+   * @return {@code true} if {@code n} is prime
+   */
+  public static boolean isPrime(int n) {
+    if (n == 2) {
+      return true;
+    }
+    if (n < 2 || n % 2 == 0) {
+      return false;
+    }
+    for (int i = 3, limit = (int) Math.sqrt(n); i <= limit; i += 2) {
+      if (n % i == 0) {
+        return false;
+      }
+    }
+    return true;
+  }
+
+  /**
+   * Calculate all the prime factors of a number and return the largest
+   *
+   * @param n integer number
+   * @return the maximum prime factor of the given number
+   */
+  static long maxPrimeFactor(long n) {
+    for (int i = 2; i < n / 2; i++) {
+      if (isPrime(i))
+        while (n % i == 0) {
+          n /= i;
+        }
+    }
+    return n;
+  }
+
+  public static void main(String[] args) {
+    int[][] testNumbers = {
+      {87, 29},
+      {10, 5},
+      {21, 7},
+      {657, 73},
+      {777, 37}
+    };
+    for (int[] num : testNumbers) {
+      assert Problem03.maxPrimeFactor(num[0]) == num[1];
+    }
+    assert Problem03.maxPrimeFactor(600851475143L) == 6857;
+  }
+}