Of course. This is a great problem that combines a huge number with a prime divisor, making it a perfect candidate for modular arithmetic.

Let the number be $N = 10^{30}$. We want to find integers Q (quotient) and R (remainder) such that:
$10^{30} = 97 \times Q + R$, where $0 \le R < 97$.

### Step 1: Find the Remainder (R)

We need to calculate $10^{30} \pmod{97}$. We can use a method called **modular exponentiation** (also known as binary exponentiation or repeated squaring).

First, let's find the remainders of powers of 1
