We want to divide \( 10^{30} \) by 97 and find the quotient and remainder.

---

### Step 1: Express the problem

\[
10^{30} = q \times 97 + r,
\]

where \(q\) is the quotient and \(r\) is the remainder, with \(0 \leq r < 97\).

---

### Step 2: Find the remainder \(r\)

Since \(10^{30}\) is large, we use modular arithmetic to find \(r = 10^{30} \bmod 97\).

We want:

\[
r \equiv 10^{30} \pmod{97}.
\]

---

### Step 3: Use properties of modular arithmetic

We'll compute powers of 10 modulo 97 using repeated squaring or stepwise multiplication:

Compute \(10^1 \bmod 97\):

\[
10^1 \equiv 10 \pmod{97}.
\]

Compute \(10^2 \bmod 97\):

\[
10^2 = 100 \equiv 100 - 97 = 3 \pmod{97}.
\]

Compute \(10^4 \bmod 97\):

\[
10^4 = (10^2)^2 = 3^2 = 9 \pmod{97}.
\]

Compute \(10^8 \bmod 97\):

\[
10^8 = (10^4)^2 = 9^2 = 81 \pmod{97}.
\]

Compute \(10^{16} \bmod 97\):

\[
10^{16} = (10^8)^2 = 81^2.
\]

Calculate \(81^2 \bmod 97\):

\[
81^2 = 6561.
\]

Divide 6561 by 97:

\[
97 \times 67 = 6499,
\]
remainder:

\[
6561 - 6499 = 62.
\]

So:

\[
10^{16} \equiv 62 \pmod{97}.
\]

---

### Step 4: Express \(10^{30}\) as \(10^{16} \times 10^{8} \times 10^{4} \times 10^{2}\):

\[
10^{30} = 10^{16 + 8 + 4 + 2} = 10^{16} \times 10^{8} \times 10^{4} \times 10^{2}.
\]

Using modular values:

\[
10^{16} \equiv 62,
\]
\[
10^{8} \equiv 81,
\]
\[
10^{4} \equiv 9,
\]
\[
10^{2} \equiv 3.
\]

Calculate stepwise modulo 97:

\[
62 \times 81 = 5022.
\]

Divide 5022 by 97:

\[
97 \times 51 = 4947,
\]
remainder:

\[
5022 - 4947 = 75.
\]

Now multiply by 9:

\[
75 \times 9 = 675.
\]

Divide 675 by 97:

\[
97 \times 6 = 582,
\]
remainder:

\[
675 - 582 = 93.
\]

Multiply by 3:

\[
93 \times 3 = 279.
\]

Divide 279 by 97:

\[
97 \times 2 = 194,
\]
remainder:

\[
279 - 194 = 85.
\]

So,

\[
r = 10^{30} \bmod 97 = 85.
\]

---

### Step 5: Find the quotient \(q\)

The quotient is:

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

Since \(10^{30}\) is \(1\) followed by 30 zeros:

\[
10^{30} = 1000000000000000000000000000000.
\]

---

### Final answer:

\[
\boxed{
\begin{cases}
\text{Quotient } q = \frac{10^{30} - 85}{97}, \\
\text{Remainder } r = 85.
\end{cases}
}
\]

---

If you want the quotient as a decimal number, it corresponds to the integer \(\frac{10^{30} - 85}{97}\).

---

### Optional: Verification step

We can check that:

\[
97 \times q + 85 = 10^{30}.
\]

---

Let me know if you'd like the quotient explicitly computed as an integer!
