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184 lines
8.0 KiB
HTML
184 lines
8.0 KiB
HTML
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<!-- Mirrored from www.mathsisfun.com/numbers/factors-all-tool.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:29:59 GMT -->
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<head>
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<!-- #BeginEditable "doctitle" -->
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<title>All Factors of a Number</title>
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<meta name="description" content="Learn how to find all factors of a numnber. Has a calculator to help you." />
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<article id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">All Factors of a Number</h1>
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<p class="center"><i>Go straight to <a href="#calc">Factors Calculator</a></i>.</p>
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<table border="0" align="center">
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<tr>
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<td valign="top">Factors are the numbers you multiply together<br />
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to get another number:</td>
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<td><img src="images/factor-2x3.svg" alt="2 and 3 are factors of 6: 2x3=6 " /></td>
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</tr>
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</table>
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<p>There can be many factors of a number.</p>
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<div class="example">
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<h3>Example: All the factors of <b>12</b></h3>
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<ul>
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<li>2 × 6 = 12, </li>
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<li>but also 3 × 4 = 12, </li>
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<li>and of course 1 × 12 = 12. </li>
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</ul>
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<p>So <b>1, 2, 3, 4, 6 and 12</b> are factors of 12. </p>
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<p>And also -1,-2,-3,-4,-6 and -12, because you get a positive number when you multiply two negatives, such as (-2)×(-6) = 12</p>
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<p>Answer: 1, 2, 3, 4, 6, 12, -1, -2, -3, -4, -6, -12</p>
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</div>
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<h3>No Fractions! </h3>
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<p>Factors are usually positive or negative <a href="../whole-numbers.html">whole numbers</a> (no fractions), so <b>½ × 24 = 12</b> is <b>not</b> listed.</p>
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<h2>All Factors Calculator<a name="calc"></a></h2>
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<p>This calculator will find <b>all</b> the factors of a number (not just the <a href="../prime-factorization.html">prime factors</a>). It works on numbers up to 4,294,967,295. Try it and see.</p>
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<script type="text/javascript">factorsallMain();</script>
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<p>Note: Negative numbers are also included, as <a href="../multiplying-negatives.html">multiplying two negatives makes a positive</a>.</p>
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<h2>How Can I Do It Myself?</h2>
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<p>Work from the outside in!</p>
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<h3>Example: All the factors of 20.</h3>
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<p><b>Start at 1</b>: 1×20=20, so put 1 at the start, and put its "partner" 20 at the other end:</p>
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<div class="beach">
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<table width="320" border="0" align="center">
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<tr align="center">
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<td width="40">1</td>
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<td> </td>
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<td width="40">20</td>
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</tr>
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</table>
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</div>
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<p><b>Then try 2</b>. 2×10=20 works, so put in 2 and 10:</p>
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<div class="beach">
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<table width="320" border="0" align="center">
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<tr align="center">
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<td width="40">1</td>
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<td width="40">2</td>
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<td> </td>
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<td width="40">10</td>
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<td width="40">20</td>
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</tr>
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</table>
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</div>
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<p><b>Then try 3</b>. 3 doesn't work (3×6=18 is too low, 3×7=21 is too high).</p>
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<p><b>Then try 4</b>. 4×5=20 works, so put them in:</p>
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<div class="beach">
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<table width="320" border="0" align="center">
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<tr align="center">
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<td width="40">1</td>
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<td width="40">2</td>
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<td width="40">4</td>
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<td> </td>
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<td width="40">5</td>
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<td width="40">10</td>
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<td width="40">20</td>
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</tr>
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</table>
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</div>
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<p>There is no whole number between 4 and 5 so you are done! (Don't forget the negative ones).</p>
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<div class="beach">
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<table width="320" border="0" align="center">
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<tr align="center">
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<td width="40">1</td>
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<td width="40">2</td>
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<td width="40">4</td>
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<td width="40">5</td>
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<td width="40">10</td>
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<td width="40">20</td>
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</tr>
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<tr align="center">
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<td>-1</td>
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<td>-2</td>
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<td>-4</td>
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<td>-5</td>
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<td>-10</td>
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<td>-20</td>
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</tr>
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</table>
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</div>
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<h2>Is That How The Calculator Works? </h2>
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<p>Actually the calculator first works out the <a href="../prime-factorization.html">prime factors</a>, then combines them together to discover all other numbers that can be multiplied to achieve your number.</p>
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<p> </p>
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<div class="related">
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<a href="../prime-composite-number.html">Prime and Composite Numbers</a>
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<a href="../prime-factorization.html">Prime Factors</a>
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<a href="../prime_numbers.html">Prime Numbers Chart</a>
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<a href="prime-factorization-tool.html">Prime Factorization Calculator</a>
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<a href="factors-multiples-table.html">Table of Factors and Multiples</a>
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<a href="../divisibility-rules.html">Divisibility Rules</a>
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</div>
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