What is the remainder when `111...111_(81)` ones is divided by 81?

What is the remainder when 111...111_(729) ones is divided by 728?

The remainder is 57 when a number is divided by 10,000. What is the remainder when the same number is divided by 1,000?

A number when divided by 16 leaves remainder 8. What is the remainder when the same number is divided by 8?

A number N when divided by 14 given the remainder 5. What is the remainder when the same number is divided by 7?

A number N when divided by 10,000 gives the remainder 57. What is the remainder when the same number is divided by 1000.

A positive integer when divided by 88 gives the remainder 61. What will be the remainder when the same number is divided by 11?