Adding Numbers to Multiples

<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-adding-numbers-to-multiples">Adding Numbers to Multiples Exercise</a></span></p><p>When you add two multiples of a certain number together, the sum will also be a multiple of that number. This is true for subtraction as well. For example, imagine we do the following:</p> <p>$$13+26=39$$</p> <p>Notice that $13$ and $26$ are both multiples of $13$. Also notice that the sum $39$ is ALSO a multiple of $13$. This might seem pretty obvious but it can be pretty tricky.&nbsp;</p> <p><span style="font-size:18px;"><strong><span style="color:#27ae60;">Tricky Example</span></strong></span></p> <p>Is the sum below prime or not prime? How do you know?</p> <p>$$30! + 29$$</p> <p>We know that $30!$ is a multiple of $29$. We also know that $29$ is a multiple of $29$. So we&#39;re adding two multiples of $29$ together, giving us a sum that is a multiple of $29$ greater than $29$. Thus, we can confidently say that this sum is&nbsp;<strong><u>not</u></strong>&nbsp;prime, even though the number is stupidly large.</p>