Consider the number N=12^{6} \times 3^{8} \times 5^{3} Which of the following statements is/are <strong>CORRECT</strong>?<br><br>1. The number of odd factors of N is 60.<br>2. The number of even factors of N is 720.<br><br>Select the correct answer using the code given below:
- A. Only 1
- B. Only 2
- C. Both 1 and 2 ✓
- D. Neither 1 nor 2
Correct Answer: C. Both 1 and 2
Explanation
N = (2^2 \times 3)^6 \times 3^8 \times 5^3 = 2^{12} \times 3^{14} \times 5^{3}. Number of odd factors (ignoring power of 2) = (14+1)(3+1) = 60. Number of even factors = 12 \times (14+1)(3+1) = 720. Both statements are correct.
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