Number Properties Puzzle – Challenge 8

Challenge:

The number 10 has four different factors: 1, 2, 5, 10. What is the smallest 2 digits number that has exactly three positive factors?

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Each prime number has exactly 2 factors, 1 and the number itself. To find the smallest 2 digits number, n, that has exactly three positive factors, we need to find an odd perfect square number. Why? 
The factors of number n are 1, n and a prime number. Let’s consider the smallest prime numbers:
2: If 2 is a factor of n, then n should be 4 (1×2×2). This is not the answer. Since, n should be a 2 digits number.
3: If 3 is a factor of n, then n should be 9 (1×3×3). This is not the answer!
5: If 5 is a factor of n, then n should be 25 (1×5×5). Bingo!

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