Level
2

A 4-digit number has exactly 3 positive factors. Find the maximum value of this 4-digit number.

The answer is 9409.

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Only perfect squares can have an odd number of factors. More importantly, only squares of

primeshave exactly $3$ factors. So we need the largest square of a prime under $10000$ . Since $\sqrt{10000}=100$ we want the largest prime under $100$ which is $97$ . The solution is $97^{2}=\boxed{9409}$