How do i solve find the remainder questions? I didn't understand the concept of (mod).Please help :)

Hi,

The modulus representation is just a convention. If the remainder obtained on dividing a by b is c, then the relation between the three variables is represented as:

a mod b = c

For example, 5 mod 2 = 1; 17 mod 5 = 2 and so on

The main point that you have to remember while solving remainder questions is that the number that is being divided can be split. For example:

20 mod 7 = ( 2 mod 7 * 10 mod 7 ) mod 7 = (2 * 3) mod 7 = 6

This is useful in finding the remainder of a number raised to a large power divided by another number.

For example: $$3^{100}$$ mod 8 = ($$3^2$$ mod 8 * $$3^2$$ mod 8 .... 50 times) mod 8

$$3^2$$ mod 8 = 9 mod 8 = 1, so $$3^{100}$$ mod 8 = (1*1*1*...50 times) mod 8 = 1 mod 8 = 1

There are a few theorems based on this concept. You can check them out here:

https://cracku.in/cat/quant-and-di/number-systems/cheatsheet