Discussion

Explanation:

Since N has 6 factors, 

6 can be factorized as 6 or 2 × 3.

∴ N must be of the form P₁⁵ or P₂ × P₃² where P₁, P₂, P₃ are prime numbers.

If N takes the form P₁⁵ then P₁ can only be 2. [10 ≤ N ≤ 50]

If N takes the form P₂ × P₃² then the possibilities are:
2 × 3², 2 × 5², 3 × 2², 5 × 2², 5 × 3², 7 × 2², 11 × 2²

So, N can take 1 + 7 = 8 values in all.

Hence, 8.

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