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

Answer and Explanation

Solution: option 1

 

Question 2 . Find remainder of (1) 32

(2) 16

(3) 8

(4) 24

Answer and Explanation

Solution: option 2

 

Question 3. Find remainder of 

(1)122

(2)16

(3)61

(4)37

Answer and Explanation

Solution: option 3

 

Question 4.  Find the remainder of

(1) 4

(2) 3

(3) 1

(4) 2

Answer and Explanation

Solution: option 3

 

Question 5. Find the remainder of

(1) 1

(2) 16

(3) 4

(4) 8

Answer and Explanation

Solution: option 4

 




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