Positive Factors with PF

<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&nbsp;in the prime factorization (in this case, we would get&nbsp;$4$, $2$, $4$)</li> <li>multiply those numbers together (in this case $4 \times 2 \times 4 = 32$)</li> </ul> <p>Here&#39;s another example. How many positive factors does $36$,$000$ have?&nbsp;</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&nbsp;<strong><u>only</u></strong><u><strong>&nbsp;one</strong></u>&nbsp;prime factor, like $7^5$, simply add $1$ to the exponent $5+1=6$ to get the total number of positive factors.</p>