The sum of the divisors of `2^(5)*3^(4)*5^(2)` is

Options

A. `3^(2).7^(1).11^(2)`
B. `3^(2).7^(1).11^(2).31`
C. `3.7.11.31`
D. none of these

Answer

B

Explanation

Any divisor of `2^(5)xx3^(4)xx5^(2)` is of the form `2^(a)xx3^(b)xx5^(c)`, where `0leale5,ble4and0lecle2`. Thus,
The sum of the divisors
`=sum_(a=0)^(5)sum_(b=0)^(4)sum_(c=0)^(2)2^(a)3^(b)5^(c)`
`=(1+2+......+2^(5))(1+3+......+3^(4))(1+5+5^(2))`
`=((2^(6)-1)/(2-1))xx((3^(5)-1)/(3-1))((5^(3)-1)/(5-1))=63xx121xx31=3^(2)xx7xx11^(2)xx31`