**Step 1:** Apply the rules to each digit of the number 6452851.

According to the Remainder Theorem, if a polynomial $P(x)$ is perfectly divisible by a linear factor $(x-c)$, then $P(c) = 0$.

This is a cryptarithmetic puzzle. We can solve it by testing the given options.

**Step 1:** The largest four-digit number is 9999.

We will use modular arithmetic. We need to find the remainder of $5^{501}$ when divided by 126.

For a number to be divisible by 3, the sum of its digits must be a multiple of 3.

This problem has two parts.

The divisibility rule for 8 states that a number is divisible by 8 if its last three digits are divisible by 8. We will check the last three digits of each number.

**Step 1:** The greatest 4-digit number is 9999.

**Step 1:** Identify the greatest three-digit number. This is 999.