Loading...
There are two cases to consider when finding the # of Multiples in an Interval:
Case 1 (From $1$ to $n$)
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 $1$,$000$?
$$\frac{1000}{31} \approx 32.26$$
We simply take the whole number $32$ to get our answer.
Case 2 (From $n$ to $m$, where $n \neq 1$)
For this case, we want to use the following formula:
$$\frac{\textrm{last multiple} - \textrm{first multiple}}{\textrm{multiple in question}} + 1$$
For example, the number of multiples of $3$ from $29$ to $112$ is
$$\frac{111 - 30}{3} + 1 = 28$$