How many factors of 24 x 37 x 52 are perfect square?
2024
How many factors of 24 x 37 x 52 are perfect square?
Answer: B. 24 — Key idea: a divisor is a perfect square exactly when every prime exponent in its factorization is even. For 2^4: even exponents possible are 0, 2, 4 → 3…
- A.
20
- B.
24
- C.
12
- D.
48
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Correct answer: B
Key idea: a divisor is a perfect square exactly when every prime exponent in its factorization is even.
For 2^4: even exponents possible are 0, 2, 4 → 3 choices.
For 3^7: even exponents possible are 0, 2, 4, 6 → 4 choices.
For 5^2: even exponents possible are 0, 2 → 2 choices.
Total perfect-square divisors = 3 × 4 × 2 = 24.
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