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
Only perfect squares can have an odd number of factors. More importantly, only squares of primes have exactly 3 factors. So we need the largest square of a prime under 1 0 0 0 0 . Since 1 0 0 0 0 = 1 0 0 we want the largest prime under 1 0 0 which is 9 7 . The solution is 9 7 2 = 9 4 0 9