2023 · Q22
Consider the following statements in respect of all factors of 360 :
- 1The number of factors is 24. 2. The sum of all factors is 1170.
Which of the above statements is/are correct?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Since 360 = 2³ · 3² · 5, the number of factors is (3 + 1)(2 + 1)(1 + 1) = 24. The sum of all factors is ((2⁴ − 1)/1) × ((3³ − 1)/2) × ((5² − 1)/4) = 15 × 13 × 6 = 1170. Both statements are correct (C).