{% extends "multiple_choice_template.html" %}
{% block maincode %}
<script language=Javascript1.2><!--

Exercise.fAddNoneOfThese = false;

var allprimes = new Array(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);
                                
var num1 = 0;                                                      //variable that holds the first number of the problem
var num2 = 0;                                                      //variable that holds the second number of the problem
var num1Factors = new Array();                                    //array that holds the prime factorization of the first number
var num2Factors = new Array();                                    //array that holds the prime factorization of the second number

var tempNumPool = new Array();                                    //temporary array for holding the half of the answer pool
var answerPool = new Array();                                     //array that holds the prime factors of both numbers and is used to generate correct and incorrect answers
var answerPoolBool;                                               //array to use with answerPool to simulate 2d array, each element is a bit setting of true or false

var factors = new Array();                                        //array for use in the supporting function that fins prime factors
var primefzn;                                                     //variable for holding the prime factorization

var answer = 1;                                                   //variable that holds the correct answer
var wrongAnswer = 1;                                              //variable that holds the incorrect answers
var answerFactors = new Array();                                  //array that holds the factorization of the answer
var combinedFactors = new Array();                                //array that holds the combined factors of the original numbers in the problem

var i = 0;                                                        //multi use counter
var j = 0;                                                        //multi use counter
var k = 0;                                                        //multi use counter
var l = 0;                                                        //multi use counter

var multiCount = 0;                                               //keeps track of the number of multiplications to use when generating answers
var primeMultiplier = 1;                                          //holds a prime number not contained within the answer pool
var lcd;                                                          //Holds the lowest common divisor of the two numbers
var lcdCount = 0;                                                 //holds the number of itmes the LCDoccurs

/***************************** Start of main code *********************************/

num1 = getRandomIntRange(4, 16);                                  //generate random numbers for the problem.  A max of 21 must be maintained.
num2 = getRandomIntRange(4, 16);                                  
while(contains(allprimes, num1))                                 
{                                                                 
    num1 = getRandomIntRange(4, 16);
}

while((contains(allprimes, num2)) || (num2 == num1))            //same loop as above, just with the second number.
{
    num2 = getRandomIntRange(4, 16);
}

tempNumPool = new Array();
find_factors(num1);                                             //We find the factors of num1 which are stored in primefzn
num1Factors = primefzn;                                         //We assign the factors to num1Factors
primefzn = null;                                               //Destroy the reference to the value, failure to do so will cause the array to keep growing in subsequent uses
for(i=0;i<tempNumPool.length;++i)                              //set the first list of available digits for multiplication to the answerpool
{
    answerPool.push(tempNumPool[i]);
}

tempNumPool = new Array();
find_factors(num2);                                             //Find factors of num2
num2Factors = primefzn;                                         //assign the factors to num2Factors
primefzn = null;                                               //Destroy reference
for(i=0;i<tempNumPool.length;++i)                              //Append the available digits into the answerpool.
{
    answerPool.push(tempNumPool[i]);
}

tempNumPool = new Array();
answer = findLCM(num1, num2);
find_factors(answer);
for(i=0;i<tempNumPool.length;++i)
{
    answerFactors.push(tempNumPool[i]);
}

primefzn = null;

i = 0;
k = 0;
answer = 1;
multiCount = getRandomIntRange(1, answerFactors.length);
answerPoolBool = new Array(answerFactors.length);
while(i < multiCount)
{
    k++;
    j = getRandomIntRange(0,answerFactors.length - 1);         //pick a random element
    if(1 != answerPoolBool[j])                                 //if not in use
    {
        answer = answer * answerFactors[j];                    //multiply it in
        answerPoolBool[j]=1;                                   //mark it as in use
        i++;                                                   //and iterate
        if( (i >= multiCount) && ((answer == num1) || (answer == num2)) )
        {
            i--;                                               //If the final operation results in the original numbers, roll back iterator
        }
    }
    if(20 <= k)                                               //if after 20 trys it cannot get a non-original number, multiply two together and break;
    {                                                         //specifically 12 and 6, and 8 and 16 will have this problem and need this break
        
        j = getRandomIntRange(0,answerFactors.length - 1);
        k = getRandomIntRange(0,answerFactors.length - 1);
        while(j == k)                                         //loop to make sure we grab different factors
        {
            k = getRandomIntRange(0,answerFactors.length - 1);
        }
        answer = answerFactors[j] * answerFactors[k];
        break;
    }
}
setCorrectAnswer(answer);                                     //set the correct answer

find_factors(answer); 
answerFactors = primefzn;                                     //find their combined factors
primefzn = null;   

find_factors(findLCM(num1, num2));                            //find factors of the numbers product
combinedFactors = primefzn;                                   //find their combined factors
primefzn = null;                                              //destroy reference

answerPoolBool = new Array(answerPool.length);                //initialize the array to act as a bool field in a 2d array
multiCount=Math.floor(answerPool.length/2);                   //will use half of the available pool in generating answers
multiCount--;                                                 //increase or decrease multicount to make larger and smaller wrong answers respectively
while(Exercise.getNumPossibleAnswers() <= 5)                              //number of wrong answers generated
{
    k++;
    i=0;                                                      //sets i to zero for each loop
    j=0;                                                      //sets j to zero for each loop
    wrongAnswer = 1;                                          //sets wrongAnswer to 1 for each loop
    answerPoolBool = new Array(answerPool.length);            //reinitializes answerPoolBool for each loop
    while(i < multiCount)
    {
        j = getRandomIntRange(0,answerPool.length - 1);       //pick a random element
        if(1 != answerPoolBool[j])                            //if not in use
        {
            wrongAnswer = wrongAnswer * answerPool[j];        //multiply it in
            answerPoolBool[j]=1;                              //mark it as in use
            i++;                                              //and iterate
        }
    }
    primeMultiplier = getRandomIntRange(2, 11);               //get a number
    while((contains(answerPool, primeMultiplier)) || (!contains(allprimes, primeMultiplier)))
    {                                                         //make sure it isn't in the answer pool and make sute it is prime
        primeMultiplier = getRandomIntRange(2, 11);
    }
    wrongAnswer = wrongAnswer * primeMultiplier;              //multiply the prime number in
    if(wrongAnswer == num1 || wrongAnswer == num2)            //if the wrong answer equalls one of the original numbers
    {
        wrongAnswer--;                                        //decrement it by one
    }
    addWrongChoice(wrongAnswer);                            //add the wrong choice to the list of them
    if(40 < k)
    {
        break;
    }
}

/***************************** End of main code *********************************/

/***************************** Start of supporting functions *********************************/
function contains(a, obj) 
{
    var i = a.length;
    while (i--) 
    {
        if (a[i] == obj) 
        {
            return true;
        }
    }
    return false;
}

function findGCD(num1, num2)
{
    var x, y, z;
    x = num1;
    y = num2;
    while (0 != y) 
    {
        z = x % y;
        x = y;
        y = z;
    }
    return x;
}

function findLCM(num1, num2)  
{
    var gcd = getGCD(num1, num2);
    var lcm = (num1 * num2) / gcd;
    return lcm;
}
function find_factors(x)
{
    if (inArray(x, allprimes)) 
    {
        if (primefzn == null) 
        {
            primefzn = x.toString();
            tempNumPool.push(x);
        } else 
        {
            primefzn = primefzn + "&times;" + x;
            tempNumPool.push(x);
        }
        return;
    }
    var maxf = Math.sqrt(x);
    for (j=2; j<=maxf; j++)
    {
        if (x % j == 0) {
            factors.push(j);
            find_factors(j);
            
            factors.push(x / j);
            find_factors(x / j);
            return;
        }
    }
}
function draw_next_step()
{
	if (Exercise.steps_given>=0)
	{
	    document.getElementById('hint1').style.display = 'block';
	    document.getElementById('hint1').innerHTML = "<li>The prime factorization of " + num1 + " is: " + num1Factors + "</li>";
	}
	if (Exercise.steps_given>=1)
	{
		  document.getElementById('hint2').style.display = 'block';
		  document.getElementById('hint2').innerHTML = "<li>The prime factorization of " + num2 + " is: " + num2Factors + "</li>";
	}
	if (Exercise.steps_given>=2)
	{
		  document.getElementById('hint3').style.display = 'block';
		  document.getElementById('hint3').innerHTML = "<li>So, any number divisible by both must have " + combinedFactors + " as part of its own prime factorization.</li>";
	}
	if (Exercise.steps_given>=3)
	{
		  document.getElementById('hint4').style.display = 'block';
		  document.getElementById('hint4').innerHTML = "<li>The prime factorization of " + answer + " is " + answerFactors + " so it is divisible into any number that has " + combinedFactors + " as part of its factorization.</li>";
	}
	Exercise.steps_given++;
}
/***************************** End of supporting functions *********************************/

//-->
</script>
{% endblock maincode %}

{% block maincell %}
<script language=Javascript1.2><!--
write_text('All numbers divisible by both `' + num1 + '` and `' + num2 + '` are also divisible by which of the following?');
/******** debug/testing outputs
write_text('Number 1 factors: ' + num1Factors);
write_text('Number 2 factors: ' + num2Factors);
write_text('Answer Pool: ' + answerPool);
write_text('Answer: ' + answer);
***************/
//-->
</script>
<br />
<ul>
<div id="hint1" style="display:none;font-family:sans-serif;font-size:12pt">Hint 1</div>
<div id="hint2" style="display:none;font-family:sans-serif;font-size:12pt">Hint 2</div>
<div id="hint3" style="display:none;font-family:sans-serif;font-size:12pt">Hint 3</div>
<div id="hint4" style="display:none;font-family:sans-serif;font-size:12pt">Hint 4</div>
</ul>

{% endblock maincell %}
{% block hintfunction %}draw_next_step(){% endblock hintfunction %}