<p><a target="_blank" href="https://www.youtube.com/watch?v=9CS7j5I6aOc" target="_blank">Mind Blown video</a></p>
<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-positive-factors-with-pf">Positive Factors with PF Exercise</a></span></p><p>To find the number of positive factors for a given integer using Prime Factorization, follow these steps:</p>
<ul>
<li>first prime factorize the integer (eg: $3000 = 2^3 \times 3^1 \times 5^3$)</li>
<li>add 1 to each exponent in the prime factorization (in this case, we would get $4$, $2$, $4$)</li>
<li>multiply those numbers together (in this case $4 \times 2 \times 4 = 32$)</li>
</ul>
<p>Here's another example. How many positive factors does $36$,$000$ have? </p>
<ul>
<li>Prime factorize: $2^53^25^3$</li>
<li>Add $1$ to each exponent: $(5+1), (2+1), (3+1)=6,3,4$</li>
<li>Multiply those numbes together:
<ul>
<li>$6 \times 3 \times 4=72$</li>
</ul>
</li>
</ul>
<p>If a certain integer has <strong><u>only</u></strong><u><strong> one</strong></u> prime factor, like $7^5$, simply add $1$ to the exponent $5+1=6$ to get the total number of positive factors.</p>