<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-of-multiples-in-interval" target="_blank"># of Multiples in Interval Exercise</a></span></p><p>There are two cases to consider when finding the <strong><span style="color:#27ae60;"># of Multiples in an Interval</span></strong>:</p>
<p><span style="font-size:18px;"><span style="color:#e74c3c;">Case 1 (From $1$ to $n$)</span></span></p>
<p>This is the easy case. You simply have to divide $n$ by the multiple in question and take the whole number result. For example, how many multiples of $31$ are there from $1$ to $1$,$000$?</p>
<p>$$\frac{1000}{31} \approx 32.26$$</p>
<p>We simply take the whole number $32$ to get our answer.</p>
<p><span style="font-size:18px;"><span style="color:#e74c3c;">Case 2 (From $n$ to $m$, where $n \neq 1$)</span></span></p>
<p>For this case, we want to use the following formula:</p>
<p>$$\frac{\textrm{last multiple} - \textrm{first multiple}}{\textrm{multiple in question}} + 1$$</p>
<p>For example, the number of multiples of $3$ from $29$ to $112$ is </p>
<p>$$\frac{111 - 30}{3} + 1 = 28$$</p>