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<!DOCTYPE html>
<html data-require="math graphie">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Prime factorization</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="cx">0</var>
<var id="y">0</var>
</div>
<div class="problems">
<div id="prime">
<div class="vars">
<var id="NUMBER">getPrime()</var>
</div>
<p class="question">What is the prime factorization of <code><var>NUMBER</var></code>?</p>
<p class="solution" data-type="primeFactorization"><var>NUMBER</var></p>
<div class="hints">
<p>Let us draw a factor tree.</p>
<div class="graphie" id="factor-tree">
init({
range: [ [-1, 2], [-1, 1] ],
scale: [30, 30]
});
label( [cx, y], NUMBER );
</div>
<div class="graphie" data-update="factor-tree">
circle( [cx, y], 0.5 );
</div>
<p>Because <code><var>NUMBER</var></code> is prime, its prime factorization is simply <code><var>NUMBER</var></code>.</p>
</div>
</div>
<div id="composite" data-weight="3">
<div class="vars">
<var id="NUMBER">getComposite()</var>
<var id="SOLUTION">getPrimeFactorization( NUMBER )</var>
<var id="FACTORIZATION">SOLUTION.slice( 0, SOLUTION.length - 1 )</var>
<var id="curr">NUMBER</var>
</div>
<p class="question">What is the prime factorization of <code><var>NUMBER</var></code>?</p>
<p class="solution" data-type="primeFactorization"><var>SOLUTION.join("x")</var></p>
<div class="hints">
<div>
<p>Let us draw a factor tree.</p>
<div class="graphie" id="factor-tree">
init({
range: [ [-1, FACTORIZATION.length + 2], [ -2 * FACTORIZATION.length - 1, 1] ],
scale: [30, 30]
});
label( [cx + 1, y], curr );
</div>
</div>
<div class="graphie" data-each="FACTORIZATION as factor" data-update="factor-tree">
path( [ [cx + 1, y - 0.5], [cx, y - 1.5] ] );
path( [ [cx + 1, y - 0.5], [cx + 2, y - 1.5] ] );
y -= 2;
cx += 1;
curr = curr / factor;
label( [cx - 1, y], factor );
circle( [cx - 1, y], 0.5);
label( [cx + 1, y], curr );
</div>
<div class="graphie" data-update="factor-tree">
circle( [cx + 1, y], 0.5);
</div>
<p>The prime factorization of <code><var>NUMBER</var></code> is <code><var>SOLUTION.join(" \\times ")</var></code>.</p>
</div>
</div>
</div>
</div>
</body>
</html>