The number of even divisors of the number N = 12600 is 

${\text{N=12600=2}}^3\times 3^2\times 5^2\times 7^1$

The number of even divisors is equal to number of ways in which one or more ‘2’ , zero or more '3', zero or more '5' and zero or more '7' can be selected, 

and is given by (3)(2+1)(2+1)(1+1)=54.