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 **

**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**