<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-factors-of-factorials">Factors of Factorials Exercise</a></span></p><p>Factorials have a <em>lot</em> of factors!</p>
<p>For example, $8!$ has the obvious factors of $8$, $7$, $6$, $5$, $4$, $3$, $2$, and $1$, but it has so many more!</p>
<p>$56$ is also a factor of $8!$ because $8 \times 7 = 56$.</p>
<p>$30$ is also a factor of $8!$ because $6 \times 5 = 30$.</p>
<p>Even $1$,$440$ is a factor of $8!$ because $8 \times 6 \times 5 \times 3 \times 2 = 1$,$440$. </p>
<p>In fact, if you convert $8!$ into its prime factorization form, $2^7 \times 3^2 \times 5^1 \times 7^1$, and you do the prime factorization trick to find the number of positive factors, you will see that $8!$ has $96$ positive factors. If you're not sure where this came from, don't worry -- it's coming later in your studies.</p>
<p>$20!$ has a mind-numblingly large $41$,$040$ positive factors!</p>