My script finds all factors of an integer. First it finds all prime integers using trial division then it uses the prime factors to find all other factors of the integer.
I would like to know how I can improve and simplify it? I think the code that prevents duplicate factors such as 4 x 5 and 5 x 4 probably could be improved but this is the simplest way I could think of.
Also, I am hoping that this is accurate and works for integers up to 99,999 but I have no idea how I could even test for that?
Your thoughts are much appreciated. Thanks.
My script on JS Bin: http://jsbin.com/arucuy/1/edit
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>All Factors 1</title>
<script>
window.onload = function() {
// Find all factors
var n = 20;
// Save the inputted number above for later use
var n2 = n;
// Store prime factors in array
var primeFactorsArray = new Array();
// Store all factors in array
var allFactorsArray = new Array();
var addFactor = true;
// Prime numbers list - saves time - currently goes up to 1,000 - not sure how high I should go if I plan on finding prime factors of integers up to 99,999?
var primeNumbers = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997];
// Trial division algorithm to find all prime factors of inputted number
for (var i = 0, p = primeNumbers[i]; i < primeNumbers.length && p * p <= n; i++, p = primeNumbers[i]) {
while (n % p == 0) {
primeFactorsArray.push(p);
n /= p;
}
}
if (n > 1) {
primeFactorsArray.push(n);
}
/////////////////////////////////////////////////////////////////////////////
// Use the prime factors above to find all the factors of the inputted number
for (var i = 0, p = primeFactorsArray[i]; i < primeFactorsArray.length; i++, p = primeFactorsArray[i]) {
// Check that the prime number isn't a duplicate
// Example: 20 = 2 x 2 x 5 --- We only want to try 2 once
if (primeFactorsArray[i] !== primeFactorsArray[i-1]) {
while (n2 % p == 0) {
otherFactor = n2 / p;
// Prevent duplicate factors
// Example: 20 --- 4 x 5 and 5 x 4 are duplicate factors of 20
for (var t = 0; t < primeFactorsArray.length; t++) {
if (otherFactor == primeFactorsArray[t]) { // if otherFactor is a prime number don't add it
addFactor = false;
} else {
addFactor = true;
}
}
if (addFactor == true) {
allFactorsArray.push(p + " x " + otherFactor);
}
p *= p;
}
}
}
// Display stuff
document.getElementById("divOutput").innerHTML += "<b>Prime factors of " + n2 + "</b><br />";
for (var i = 0; i < primeFactorsArray.length; i++) {
document.getElementById("divOutput").innerHTML += primeFactorsArray[i];
// Prevent extra x
if (i + 1 < primeFactorsArray.length) {
document.getElementById("divOutput").innerHTML += " x ";
}
};
document.getElementById("divOutput").innerHTML += "<br /><b>All factors of " + n2 + "</b><br />";
for (var i = 0; i < allFactorsArray.length; i++) {
document.getElementById("divOutput").innerHTML += allFactorsArray[i] + "<br />";
};
}
</script>
</head>
<body>
<div id="divOutput"></div>
</body>
</html>
