Test if number is prime or not, and find numbers divisors

Some integers can be divided evenly into several parts, but some are not. Number N that cannot be divided into any number of parts except for N itself, is called a prime number. Fundamental theorem of arithmetic states that every composite (non-prime) number N can be represented as a product of several lesser prime numbers p_i, and the set of these prime numbers is uniquely linked with N. Script on this webpage searches any prime divisors for the given N (a process called factorization) and therefore can be used to determine whether some integer is prime or not.

Test for primality

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          function findDivisors(n, includeSelf){
              includeSelf = includeSelf || false;
              if (n == 1) {
                  return [];
              }
              var maxDiv = Math.ceil(Math.sqrt(n));
              var divisors = [];
              for (var p = 2; p <= maxDiv; p++) {
                  if (n % p == 0) {
                      q = n / p;
                      divisors.push(p);
                      divisors = divisors.concat(findDivisors(q, true));
                      if (divisors.reduce(function(a, b) { return a*b }) == n) {
                          return divisors;
                      }
                  }
              }
              if (includeSelf) {
                  divisors.push(n);
              }
              return divisors;
          }
  
          $(document).ready(function(){
  
             $(".btn-test").click(function(){
                 var num = parseInt($("#num").val(), 10);
                 var box = $("#result");
                 if (isNaN(num)) {
                     box.html("Invalid number");
                 } else if (num < 1) {
                     box.html("Only positive number can be checked!");
                 } else {
                     box.html("Checking in progress...");
                     var result = findDivisors(num, false);
                     if (result.length > 0) {
                         box.html(num + " <strong>is NOT prime</strong>! Prime divisors: <strong>" + result.join(" x ") + " = " + num + "</strong>");
                      } else {
                         box.html(num + " <strong>is prime</strong>! No divisors except 1 and " + num);
                      }
                 }
                 box.trigger("autoresize");
             });
  
           });