Question

The number of positive divisors of $768$ is

• A. 17
• B. 18
• C. 19
• D. 20

Answer 1

Answer: (B)

18

$768=2^8\times 3$
The positive divisor of $768$ can be any of the term of the expansion $(2^0+2^1+2^2+......2^8)(3^0+3^1)$
Hence, total number of positive divisors $=$ $\left(\begin{array}{c}9\\ 1\end{array}\right)\left(\begin{array}{c}2\\ 1\end{array}\right)=18$