Correct Answer - Option 1 : 3.13
Given:
900
Formula used:
Sum of reciprocal of all factors = Sum of all factors/number
Concept used:
If k = ax × by, then
Sum of all factors = (a0 + a1 + a2 + ….. + ax) (b0 + b1 + b2 + ….. + by)
Calculation:
900 = 22 × 32 × 52
Sum of all factors = (20 + 21 + 22) (30 + 31 + 32) (50 + 51 + 52)
⇒ (1 + 2 + 4) (1 + 3 + 9) (1 + 5 + 25)
⇒ 7 × 13 × 31
⇒ 2821
Sum of reciprocal of all factors = 2821/900
⇒ 3.13
∴ required answer is 3.13
