803661374160 = 73^2 *37^2* 17^1 * 5^1 * 3^4 * 2^4

Any factor of this number should be of the form 73^a * 37^b * 17^c * 5^d * 3^e * 2^f

For the factors of this number to be an even number f should be non 0

a can take values 0, 1, 2,

b can take values 0, 1, 2

c can take values 0, 1

d can take values 0, 1

e can take value 0, 1, 2, 3, 4

f can take value 1, 2, 3, 4

Total number of even factors = 3*3*2*2*5*4= 720