Correct Answer - Option 4 :
\(\frac{5}{{64}}\)
Given:
HCF = 16
Product of numbers = 1024
Concept used:
The reciprocal of the number is 1 divided by the number
Ex:- The reciprocal of n = 1/n
Calculation:
Let the number be 16a and 16b
16a × 16b = 1024
ab = 4
Co-prime factors of 4
(1, 4)
The number will be 16 and 64
Sum of the number = 16 + 64 = 80
Sum of their reciprocal
⇒ (1/16) + (1/64)
⇒ (80/1024) = 5/64
∴ The sum of the reciprocals of numbers is 5/64.