Consider the following statements in respect of all factors of 360 :<br>1. The number of factors is 24.<br>2. The sum of all factors is 1170.<br>Which of the above statements is/are correct?
- A. 1 only
- B. 2 only
- C. Both 1 and 2 ✓
- D. Neither 1 nor 2
Correct Answer: C. Both 1 and 2
Explanation
Prime factorization of 360 = 2^3 \times 3^2 \times 5^1. The number of factors is (3+1)(2+1)(1+1) = 24. The sum of factors is (2^0+2^1+2^2+2^3)(3^0+3^1+3^2)(5^0+5^1) = 15 \times 13 \times 6 = 1170. Both statements are correct.
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