We want integers \(q,r\) such that
\[
10^{30} = 97q + r,\quad 0 \le r < 97.
\]

Compute \(10^{30} \bmod 97\) using repeated squaring (mod 97):

- \(10^1 \equiv 10\)
- \(10^2 \equiv 100 \equiv 3\)
- \(10^4 \equiv 3^2 = 9\)
- \(10^8 \equiv 9^2 = 81\)
- \(10^{16} \equiv 81^2 = 6561 \equiv 6561 - 97\cdot67 = 6561 - 6499 = 62\)

Now:
\[
10^{30} = 10^{16} \cdot 10^{8} \cdot 10^{4} \cdot 10^{2}
\]
so
\[
10^{30} \equiv 62 \cdot 81 \cdot 9 \cdot 3 \pmod{97}.
\]

Step by step:

- \(62 \cdot 81 = 5022 \equiv 5022 - 97\cdot51 = 5022 - 4947 = 75\)
- \(75 \cdot 9 = 675 \equiv 675 - 97\cdot6 = 675 - 582 = 93\)
- \(93 \cdot 3 = 279 \equiv 279 - 97\cdot2 = 279 - 194 = 85\)

So
\[
10^{30} \equiv 85 \pmod{97},
\]
hence the remainder is \(r = 85\).

Now
\[
q = \frac{10^{30} - 85}{97}.
\]

Since \(10^{30} = 1{,}000{,}000{,}000{,}000{,}000{,}000{,}000{,}000{,}000\),

\[
q = 1030927835051546391752577319587.
\]

Answer:

- Quotient: \(1030927835051546391752577319587\)
- Remainder: \(85\)
