Puzzle for the day!

[complicatedliar]

Given that 37! = 13763753091226345046315979581abcdefgh0000000, determine, with a minimum of arithmetical effort, the digits a, b, c, d, e, f, g, and h.

Calculators are cheating, dear ones. And cheaters never win.

First to find the solution shall be monarch for the day!

Comments

[skeletonenigma]

a = 5
b = 8
c = 0
d = 9
e = 0
f = 2
g = 4
h = 0

I'm not too interested in being a monarch. Your acknowledgment of my brilliance will be more than enough.