How many -digit natural numbers are completely divisible by ?
Step 1: Condition for divisibility by
A number is said to be divisible by when its last two digits are divisible by .
For example, let us consider a random number .
The last two digits are .
We know that , hence is divisible by .
Therefore is divisible by .
Step 2: Estimate the count of natural numbers
Let us enlist such -digit natural:
There are a total of digits in this range.
Hence, the number of -digit natural numbers that are completely divisible by is .