We can start writing out the Fibonacci sequence and find a pattern for the remainders when divided by 8.
1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, ...
We notice that the pattern repeats every 6 terms.
Since $100 \div 6 = 16$ with a remainder of 4, we can conclude that the remainder when the 100th term is divided by 8 is the same as the remainder when the 4th term is divided by 8, which is $\boxed{3}$.
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, $\ldots$ where the first and second terms are 1 and each term after that is the sum of the previous two terms. What is the remainder when the $100^{\mathrm{th}}$ term of the sequence is divided by 8?

### Answer:
