2022 · Q21
Consider the number N = 12⁶ × 3⁸ × 5³. Which of the following statements is/are correct?1. The number of odd factors of N is 60.2. The number of even factors of N is 720.Select the correct answer using the code given below :
Elementary MathematicsNumber System
- AOnly 1
- BOnly 2
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
N = 12⁶·3⁸·5³ = 2¹²·3¹⁴·5³. Odd factors come from 3¹⁴·5³: (14+1)(3+1) = 60, so statement 1 is correct. Total factors = 13×15×4 = 780, so even factors = 780 − 60 = 720, and statement 2 is also correct. The keyed option is C.