To determine the remainder when $538261145681367996408$ is divided by 4, we can use the divisibility rule for 4.

Divisibility rule for 4:

• A number is divisible by 4 if its last two digits are divisible by 4.

Steps:

1. Look at the last two digits of the number $538261145681367996408$. The last two digits are $08$.
2. Now, divide $08$ by 4:
   $08 \div 4 = 2$ Since $08$ is divisible by 4, the remainder is $0$.

Thus, the remainder when $538261145681367996408$ is divided by 4 is 0.

Would you like more details or have any questions?

Here are some related questions:

1. What is the remainder when a number ending in 52 is divided by 4?
2. How would the remainder change if the last two digits were 15 instead of 08?
3. Can you explain the divisibility test for 8 and how it differs from the test for 4?
4. What is the smallest number greater than 538261145681367996408 that gives the same remainder when divided by 4?
5. How can the concept of modular arithmetic be applied to this problem?

Tip: When working with divisibility rules, focus only on the relevant part of the number, like the last digits for 4 or 8.