The integer version solution is 32 threes and a four.
332 * 4 = 7,412,080,755,407,364
The reason threes work so well is because they're closest to e. The solution to the real version is to take all e's, except that 100 isn't divisible by e. (100/37) is closest.
(100/35)35 = 9,070,233,087,628,002
(100/36)36 = 9,399,612,886,687,350
(100/37)37 = 9,474,061,716,781,814
(100/38)38 = 9,294,442,148,136,202