It seems like part of your query is missing, particularly the condition regarding what the 4-digit number is divisible by. If you can provide the missing condition, I can help you find the 4-digit number.

In the meantime, here's how we would approach the problem in general:

Given:

• The 4-digit number is represented as $\overline{a347}$, where $a$ is the unknown digit.
• The number is divisible by some specific value (e.g., 9, 11, etc.).

Once we know the divisibility condition, we can determine the possible values for $a$.

Would you like to provide the missing condition? Or should I consider the most common cases, like divisibility by 9 or 11?

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Here are some questions to expand on the problem:

1. Is the number divisible by 9, 11, or another number?
2. Could $a$ be a non-zero digit?
3. How do we handle multiple possibilities if the condition allows more than one solution?
4. Would you like a detailed explanation of divisibility rules?
5. Should we consider divisibility by 2, 3, or other basic factors?

Tip: Understanding divisibility rules can simplify checking if a number is divisible by another without performing the actual division.