/**
 * Return array of prime factors (in ascending order) of n.
 * 
 * We will represent even powers of 2 as 4, for ease of plotting
 * 
 * Examples:
 *    primeFactors(1) = []
 *    primeFactors(10) = [2, 5]
 *    primeFactors(5) = [5]
 *    primeFactors(60) = [4, 3, 5]
 */
function primeFactors(n) {
  if (n < 1) throw "Argument error";
  var result = [];
  while (n != 1) {
    var factor = getFactor(n); // call getFactor function
    result.push(factor);
    n /= factor;
  }
  return result;
}


/** 
 * Return smallest prime factor of n.
 */
function getFactor(n) {
  if (n < 2) throw "Argument error";
  if (n % 4 == 0) return 4;
  if (n % 2 == 0) return 2;
  for (var i = 3; i <= Math.floor(Math.sqrt(n)); i += 2) {
    if (n % i == 0) return i;
  }
  return n;
}


/**
 * Print string representation of array of prime factors
 * Examples
 *    printFactors([4, 3, 5]) = "2 × 2 × 3 × 5"
 *    printFactors([3, 5]) = "3 × 5"
 *    printFactors([7]) = "prime"
 */
 function printFactors(factors) {
   var string = "";
   if (factors.length == 1) {
     string = factors[0] == 4 ? "2 × 2" : "prime";
     return string;
   }
   
   factors.forEach(function(factor) {
     stringFactor = factor == 4 ? "2 × 2" : factor;
     string += stringFactor + " × ";
   });
   return string.slice(0, -2);  // remove last two characters
 }