Question

The total number of all proper factors of $75600$ is

• A. $120$
• B. $119$
• C. $118$
• D. none of these

Answer 1

Answer: (C)

$118$

$75600$

$\left(765\right)\left(100\right)$

$=756(5^2\times 2^2)=(2{)}^2\times (3{)}^3\times 7(5^2\times 2^2)=(2{)}^4\times (3{)}^3\times (5{)}^2\times 7$

Therefore total number of factors :

$(4+1)(3+1)(2+1)(1+1)-2$

{$-2$ becausse one and itself are to be substracted}

$=120-2=118$