Question

The sum of all the divisors of $2^5{3}^4{5}^2$ is

• A. $3^2{.7}^2{.11}^2$
• B. $3^2.7{.11}^2.31$
• C. $\mathrm{3.7.11.31}$
• D. None of these

Answer 1

Answer: (B)

$3^2.7{.11}^2.31$

There will be $(5+1)(4+1)(2+1)=90$ divisors.

The sum of all the divisors is

$(2^0+2^1+2^2+...+2^5)(3^0+3^1+3^2+...+3^5)(5^0+5^1+5^2)$

$=\frac{2^6-1}{2-1}.\frac{3^5-1}{3-1}.\frac{5^3-1}{5-1}$ $($sum of $G.P.)$

$=63\times 121\times 31=3^2.7.{11}^2.31$