Finding Remainders of Other Integers

To find the remainder of a number when divided by a composite number (like 6, 12, or 18), you can find the remainders for its prime factors and then find a number that satisfies both (or all) conditions. This is an application of the Chinese Remainder Theorem.

For $556677 \div 6$:
1. Remainder when divided by 2: The number is odd, so remainder is 1.
2. Remainder when divided by 3: Sum of digits is 36, which is divisible by 3, so remainder is 0.
3. Find a number less than 6 that is odd and divisible by 3. The only such number is 3.