I need to divide 10^30 by 97 and find the quotient and remainder.

## Finding the Remainder

I'll use modular arithmetic to find 10^30 mod 97.

First, let me find the pattern of powers of 10 mod 97:
- 10^1 ≡ 10 (mod 97)
- 10^2 ≡ 100 ≡ 3 (mod 97)
- 10^3 ≡ 30 (mod 97)
- 10^4 ≡ 300 ≡ 9 (mod 97)
- 10^5 ≡ 90 (mod 97)
- 10^6 ≡ 900 ≡ 27 (mod 97)
- 10^7 ≡ 270 ≡ 76 (mod 97)
- 10^8 ≡ 760 ≡ 81 (mod 97)
- 10^9 ≡ 810 ≡ 34 (mod 97)
- 10^10 ≡ 340 ≡ 49 (mod 97)

Continuing this process (or using Fermat's Little Theorem where 10^96 ≡ 1 mod 97):

Let me compute 10^30 more systematically:
- 10^10 ≡ 49 (mod 97)
- 10^20 ≡ 49^2 = 2401 ≡ 2401 - 24×97 = 2401 - 2328 = 73 (mod 97)
- 10^30 ≡ 10^20 × 10^10 ≡ 73 × 49 = 3577 (mod 97)

3577 ÷ 97 = 36 remainder 85 (since 36 × 97 = 3492)

So **remainder = 85**

## Finding the Quotient

The quotient is:
$$Q = \frac{10^{30} - 85}{97}$$

Performing the division:

$$Q = 10309278350515463917525773195$$

## Final Answer

- **Quotient:** 10,309,278,350,515,463,917,525,773,195
- **Remainder:** 85
