To divide \( 10^{30} \) by \( 97 \), we can start by calculating the quotient and remainder using the division algorithm.

1. **Calculating \( 10^{30} \mod 97 \)**:  
   We can use properties of modular arithmetic and the method of successive squaring.

   First, compute some powers of \( 10 \) modulo \( 97 \):

   - \( 10^1 \equiv 10 \mod 97 \)
   - \( 10^2 \equiv 100 \equiv 3 \mod 97 \)
   - \( 10^4 \equiv 3^2 \equiv 9 \mod 97 \)
   - \( 10^8 \equiv 9^2 \equiv 81 \mod 97 \)
   - \( 10^{16} \equiv 81^2 \equiv 6561 \equiv 48 \mod 97 \)

   Now combine these to find \( 10^{30} \):
   \[
   10^{30} = 10^{16} \cdot 10^{8} \cdot 10^{4} \cdot 10^{2} = 48 \cdot 81 \cdot 9 \cdot 3
   \]

   We can compute this step by step and reduce modulo \( 97 \):
   - First, \( 48 \cdot 81 \equiv 3888 \mod 97 \):
     \[
     3888 \div 97 \approx 40.1 \implies 3888 - 40 \cdot 97 = 3888 - 3880 = 8 \implies 48 \cdot 81 \equiv 8 \mod 97
     \]

   - Next, compute \( 8 \cdot 9 \equiv 72 \mod 97 \):
   - Finally, \( 72 \cdot 3 \equiv 216 \mod 97 \):
     \[
     216 \div 97 \approx 2.2 \implies 216 - 2 \cdot 97 = 216 - 194 = 22 \implies 72 \cdot 3 \equiv 22 \mod 97
     \]

   Therefore,
   \[
   10^{30} \mod 97 \equiv 22
   \]

2. **Finding the quotient**:
   Using the fact that \( 10^{30} = 97q + r \) where \( r = 10^{30} \mod 97 \) (which is 22), we can write:
   \[
   10^{30} = 97q + 22
   \]
   Rearranging gives:
   \[
   97q = 10^{30} - 22
   \]

   Dividing \( 10^{30} \) by \( 97 \):
   \[
   q = \frac{10^{30} - 22}{97}
   \]

Since \( 10^{30} \) is a large number, the quotient will be:
\[
q = \lfloor \frac{10^{30}}{97} \rfloor
\]

Approximating \( \frac{10^{30}}{97} \) gives us:

\[
10^{30} \div 97 \approx 1.03092783505 \times 10^{28}
\]

So we can write the result as:
\[
\text{Quotient } q \approx 1.03092783505 \times 10^{28}
\]
and knowing that \( r = 22 \).

**Final result**:
- Quotient \( q \) is \( 1.03092783505 \times 10^{28} \) (exact value would be calculated more precisely if needed),
- Remainder \( r = 22 \).
