The number of proper divisors of the number obtained by dividing 13! with 100 is 
 

$13!=2^{10}{3}^5{5}^2{7}^1{11}^1$

$\frac{13!}{100}=2^8{3}^3{7}^1{11}^1$

Number of divisors=(1+8)(1+5)(1+1)(1+1)=216

Number of proper divisors=216-2=214