Question

How many $3$-digit natural numbers are completely divisible by $5$?

Answer 1

Step 1: Condition for divisibility by $5$

A number is said to be divisible by $5$ when its last digit is $5$ or $0$.

For example, let us consider a random number $425$.

The last digit is $5$.

Hence $425$ is divisible by $5$.

Step 2: Estimate the count of natural numbers

Let us enlist such $3$-digit natural:

smallest $3$-digit natural number which is divisible by $5$ is $100$.

Largest $3$-digit natural number which is divisible by $5$ is $995$.

$$\begin{gathered} a=100,d=5,a_n=995 \\ {a}_n=a+(n-1)d \\ \therefore 995=100+(n-1)5 \\ \therefore 895=5n-5 \\ \therefore 900=5n \\ \therefore n=180 \end{gathered}$$

There are a total of $180$ digits in this range.

Hence, the number of $3$-digit natural numbers that are completely divisible by $5$ is $180$.