<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. </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'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 <strong><u>not</u></strong> prime, even though the number is stupidly large.</p>