Question

For the proper divisors of $360$, the correct option(s) is/are

• A. mean is $35.21$
• B. mean is $26.78$
• C. median is $18$
• D. median is $19$

Answer 1

Answer: (A), (C)

The correct options are
A mean is $35.21$
C median is $18$

$360=2^3\times 3^2\times 5$
Sum of all proper divisors$=(1+2+2^2+2^3)(1+3+3^2)(1+5)-360=810$
Number of proper divisors $=(3+1)(2+1)(1+1)-1=23$

$\therefore$ mean $=\frac{810}{23}=35.21$
Proper divisors are $1,2,3,4,5,6,8,9,10,12,15,18,20,\cdots ,180$
$\therefore$ median $=12th$ term $=18$