Question

The sum of the divisors of $2^3.3^4{.5}^2$ is:

• A. 15625
• B. 1234
• C. 56265
• D. 56789

Answer 1

Answer: (C)

56265

Any divisor of $2^3{.3}^4{.5}^2$ is of the form $2^a{.3}^b{.5}^c$ where $0\le a\le 3,0\le b\le 4$ and $0\le c\le 2$ Thus, the sum of the divisors of $2^3{.3}^4{.5}^2$ is
$(1+2+....+2^3)(1+3+....+3^4)(1+5+5^2)=\frac{(2^4-1)(3^5-1)(5^3-1)}{(2-1)(3-1)(5-1)}=\frac{15\times 242\times 124}{1\times 2\times 4}=56265$