Question

Number of proper divisors of the number $2520$ is :

• A. $40$
• B. $44$
• C. $46$
• D. $48$

Answer 1

The correct option is C $46$

Prime factors of
$2520=2^3{3}^2{5}^1{7}^1=2^a{3}^b{5}^c{7}^d$
$\therefore$ Total number of divisors
$=(a+1)(b+1)(c+1)(d+1)$
$=\left(4\right)\left(3\right)\left(2\right)\left(2\right)=48$
And proper divisors of $2520$ are except $1$ and the number itself
$\therefore$ Required number of proper divisors $=48-2=46$
Hence (c) is correct answer.