3 Factors

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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1 solution

Jeremy Galvagni
Aug 20, 2018

Only perfect squares can have an odd number of factors. More importantly, only squares of primes have exactly 3 3 factors. So we need the largest square of a prime under 10000 10000 . Since 10000 = 100 \sqrt{10000}=100 we want the largest prime under 100 100 which is 97 97 . The solution is 9 7 2 = 9409 97^{2}=\boxed{9409}

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