Question # The number of odd proper divisors of 5040 , is

# The number of odd proper divisors of 5040 , is

(a) 12

(b) 10

(c) 11

(d) none of these

Solution

We have,

( 5040=2^{4} times 3^{2} times 5 times 7 )

( therefore quad ) Number of odd proper divisors

= Number of ways of selecting any number of ( 3^{text {'s }} ) out

two ( 3^{prime prime}, ) any number of ( 5^{prime s} ) and ( 7^{prime prime} )

[

=(2+1)(1+1)(1+1)-1=11

]