In the previous article, we discussed 2 ways to find remainders. Now, we’ll look at more methods to find remainders.

In this article, we will discuss 3 important theorems that make finding remainders very easy and simple.

Method of finding Remainder by Euler’s, Fermat’s little theorem , Wilson’s theorem

1. Euler’s Theorem:

According to the Euler’s theorem, if is divided by  f  where ( N and f are co-prime to each other and is = total co-primes less than f  ) , remainder will always be 1 .we can write it as follows Solution:

Step 1: Solution:

Step 1:  Example: Find the remainder of Solution:

Since 7 is a prime number  hence from Fermat’s little theorem . Solution: Try out some more questions based on this concept so as to get a good hold of this topic.

EXERCISE:

Question 1. Find the remainder of (1) 32

(2) 16

(3) 8

(4) 24

Solution: option 1 Question 2 . Find remainder of (1) 32

(2) 16

(3) 8

(4) 24

Solution: option 2 Question 3. Find remainder of (1)122

(2)16

(3)61

(4)37

Solution: option 3 Question 4.  Find the remainder of (1) 4

(2) 3

(3) 1

(4) 2

Solution: option 3 Question 5. Find the remainder of (1) 1

(2) 16

(3) 4

(4) 8

Solution: option 4    