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 digit is or .
For example, let us consider a random number .
The last digit is .
Hence is divisible by .
Step 2: Estimate the count of natural numbers
Let us enlist such -digit natural:
smallest -digit natural number which is divisible by is .
Largest -digit natural number which is divisible by is .
There are a total of digits in this range.
Hence, the number of -digit natural numbers that are completely divisible by is .