10^30 = 97·10309278350515463917525773195 + 85.

So the quotient is 10309278350515463917525773195 and the remainder is 85.

(Indeed 10^30 ≡ 85 (mod 97); one way: 10^2 ≡ 3, so 10^30 = 10^(16+8+4+2) ≡ 62·81·9·3 ≡ 85 (mod 97).)
