100. The teacher gives prizes to the winning students. The first student takes 1 prize and $\frac{1}{10}$ of the remaining prizes, the second student takes 2 prizes and $\frac{1}{10}$ of the remaining prizes, the third student takes 3 prizes and $\frac{1}{10}$ of the remaining prizes, and so on. Until all the prizes are taken, it is found that each student who received a prize received an equal number of prizes. The total number of prizes is $\qquad$ pieces, and the number of winning students is $\qquad$ people.
Reference answer: 81, 9