Single correct option
How many divisors of N = 2⁴ × 3³ × 5² are perfect squares?
- A. 10
- B. 12
- C. 18
- D. 24
Show answer and solution
Answer: (B) 12
A divisor 2ᵃ3ᵇ5ᶜ is a perfect square exactly when a, b, c are all even.
a ∈ {0, 2, 4} → 3 choices; b ∈ {0, 2} → 2 choices; c ∈ {0, 2} → 2 choices.
Number of square divisors = 3 × 2 × 2 = 12.
(Total divisors are 5 × 4 × 3 = 60, so 60 is not the answer; 18 would wrongly allow b = 3.)
a ∈ {0, 2, 4} → 3 choices; b ∈ {0, 2} → 2 choices; c ∈ {0, 2} → 2 choices.
Number of square divisors = 3 × 2 × 2 = 12.
(Total divisors are 5 × 4 × 3 = 60, so 60 is not the answer; 18 would wrongly allow b = 3.)
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