<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-non-factors-of-factorials" target="_blank">NON Factors of Factorials Exercise</a></span></p><p>As stated previously, factorials have A LOT of factors. So how do we find values that are NOT factors of a factorial? Let's say for example we're trying to find the smallest integers that are not factors of $20!$.</p>
<ul>
<li><strong>Step 1</strong>: Simply find the prime numbers greater than $20$.</li>
</ul>
<p style="text-align: center;">$23, 29, 31, 37, 41$, etc. are all NOT factors of $20!$</p>
<ul>
<li><strong>Step 2</strong>: But what if we want to find the non-prime non-factors? In this case, you simply need to find the multiples (greater than the number itself) of our previously identified primes:</li>
</ul>
<p style="text-align: center;"><span style="color:#27ae60;">$23$</span>: $46, 69, 92...$</p>
<p style="text-align: center;"><span style="color:#27ae60;">$29$</span>: $58, 87, 116...$</p>
<p>You get the idea. <strong>NOTE</strong> that this trick really only works for factorials greater than or equal to $10!$. If it's a small factorial, you're better off finding the factors using a more brute-force, list them all out approach.</p>