GG.27 One number after another is multiplied from 1

Numbers are being multiplied as follows.
Multiplying 1 by 2 first and multiply 3 to the product and further multiply 4 to the product--------.
Thus, one number after another is multiplied sequentially from 1.

Answer the following questions.

(1) When multiplied to a certain number, the multiplied product number contain four 0 continuously located in a line from one digit.
Find the smallest number in what is considered as a certain number.

(2) When multiplied to a certain number, the multiplied product number contain seven 0 continuously located in a line from one digit.
Find the smallest number in what is considered as a certain number.

Moreover, when you multiply from 1 to the number, find the number of 8th digit counted from one digit.




Answer
(1) 20
(2) 30, 8