Given a positive integer n, find the smallest integer which has exactly the same

It seems the question was cut off. However, I'll provide a general approach based on finding the smallest integer with a specific property, such as having the same number of digits or factors as another integer.

If the task is to find the smallest integer that has exactly the same number of digits as a given positive integer $n$:

1. Break Down the Problem

• Identify the number of digits in $n$.
• Determine the smallest integer with the same number of digits.

2. Relevant Concepts

• The number of digits $d$ in a positive integer $n$ can be found using: $d = \lfloor \log_{10}(n) \rfloor + 1$
• The smallest integer with $d$ digits is $10^{(d-1)}$.

3. Analysis and Detail

1. Calculate the number of digits $d$ in $n$.
2. Compute the smallest integer with $d$ digits using $10^{(d-1)}$.

4. Verify and Summarize

• Ensure that the computed integer truly has the same number of digits as $n$.

Final Answer

If $n$ has $d$ digits, then the smallest integer with the same number of digits is $10^{(d-1)}$. For example, if $n = 345$ (which has 3 digits), the smallest integer with 3 digits is $100$.