Remainder Properties

Important

Properties of Remainders

1. The value of remainders can be from 0 to d-1, where d is the divisor. For example, 24 divided by 5 has a remainder of 4, and when any number is divided by 5, the remainder can be from 0 to 4.

2. If N < d, the given number is less than the divisor, then the remainder will be equal to N. For ex, if 5 is divided by 7, the remainder will be 5.

3. (M + N) mod d = (M mod d + N mod d) Mod d

4. (M - N) mod d = (M mod d - N mod d) Mod d

5. (M x N) mod d = (M mod d  X N mod d ) Mod d

      Question 1

      When $$3^{333}$$ is divided by 11, the remainder is

      Question 2

      When $$10^{100}$$is divided by 7, the remainder is

      Question 3

      If $$10^{68}$$ is divided by 13, the remainder is

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