Question

The sum of all the proper divisors of 9900 is

• A. 33851
• B. 23952
• C. 23951
• D. none of these

Answer 1

The correct option is C 23951

Let $y=9900=2^2\times 3^2\times 5^2\times 11$
Hence sum of all proper divisors of $y$ is $=\frac{2^3-1}{2-1}\times \frac{3^3-1}{3-1}\times \frac{5^3-1}{5-1}\times \frac{{11}^2-1}{11-1}-2^2\times 3^2\times 5^2\times 11-1$
$=33852-9900-1=23951$