The total number of proper divisors of 38808, is  

 

Factorizing the given number, we obtain 

    $38808=2^3\times 3^2\times 7^2\times 11$

The total number of divisors of this number is same as the

number of ways of selecting some or all of two 2' s, two 3' s,

 two 7's and one 11. Therefore 

  The total number of divisors 

 $-(3+1)(2+1)(2+1)(1+1)-1=71$ 

  But, this includes the division by the number itself.

   Hence, the required number of divisors $= 71 - 1 = 70.$