## Even and Odd Numbers

## Types of Numbers on the basis of divisibility by 2

On the basis of divisibility by 2, the numbers can be divided into two groups, these two groups are**even numbers**and

**odd numbers**.

### Even Numbers

**Definition of Even Numbers**: Numbers divisible by 2 are called the **Even Numbers**.

**Alternate Definition of Even Numbers**: In other words, the multiples of 2 are called the **Even Numbers**.

**Example**: 2, 4, 6, 8, 10, 12, 14, . . . . etc. are the examples of **Even Numbers**.

**Question**: Which is the smallest even number?

**Answer**: 2 is the smallest even number.

### Consecutive Even Numbers

The odd numbers comes just after a given even number is called the **Consecutive Even Number.**

Since there is a difference of 2 between two even numbers, thus we can find as many consecutive even numbers by adding 2 to an even number.

**Example**

2, 4, 6, 8, 10, 12, 14, . . . . . are the examples of some consecutive even numbers.

#### Even Predecessor of an Even Number

The even number comes just before a given even number is called the even predecessor of that even number.

**Example:**

(a) The even number 2 comes just before the even number 4.

#### Finding the Even Predecessor of an Even Number

We can find the even predecessor of a given even number by subtracting 2 from it.

**Example: Finding the even predecessor of a given Even Numbers**

(a) Find the even predecessor of 4

= 4 – 2 = 2

Thus, the even predecessor of 4 = 2

(b) Find the even predecessor of 8

= 8 – 2 = 6

Thus, the even predecessor of 8 = 6

(c) Find the even predecessor of 12

= 12 – 2 = 10

Thus, the even predecessor of 12 = 10

(d) Find the even predecessor of 16

= 16 – 2 = 14

Thus, the even predecessor of 16 = 14

(e) Find the even predecessor of 30

= 30 – 2 = 28

Thus, the even predecessor of 30 = 28

(f) Find the even predecessor of 40

= 40 – 2 = 38

Thus, the even predecessor of 40 = 48

(g) Find the even predecessor of 58

= 48 – 2 = 46

Thus, the even predecessor of 48 = 46

(h) Find the even predecessor of 46

= 46 – 2 = 44

Thus, even predecessor of 46 = 44

### Even Successor of an Even Number

The even number comes just after a given even number is called the **Even Successor of an Even Number**

**Examples**:

The even number 4 comes just after the even number 2, hence 4 is the even successor of the even number 2.

Similarly, the even number 6 comes just after the even number 4, hence 6 is the even successor of the even number 4.

Similarly, the even number 10 comes just after the even number 8, hence 10 is the even successor of the even number 8.

#### Finding the Even Successor of an Even Number

There is a gap of 2 between two consecutive even numbers. Hence, an even successor of an even number can be got by adding 2 to the given even number.

**Example**

(a) Find the even successor of the even number 10.

**Solution**

The even successor of the even number 10

= 10 + 2 = 12

Thus, 12 is the even successor of even number 10.

(b) Find the even successor of the even number 12.

**Solution**

The even successor of the even number 12

= 12 + 2 = 14

Thus, 14 is the even successor of even number 12.

(c) Find the even successor of the even number 24.

**Solution**

The even successor of the even number 24

= 24 + 2 = 26

Thus, 26 is the even successor of even number 24.

(d) Find the even successor of the even number 36.

**Solution**

The even successor of the even number 36

= 36 + 2 = 38

Thus, 38 is the even successor of even number 36.

(e) Find the even successor of the even number 100.

**Solution**

The even successor of the even number 100

= 100 + 2 = 102

Thus, 102 is the even successor of even number 100.

### Odd Numbers

Numbers which are not divisible by 2 are known as **Odd Numbers**.

In other words, the numbers other than the multiples of 2 are known as **Odd Numbers.**

**Example**: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, . . . .

**Question** Which is the smallest odd number?

**Answer**: 1 is the smallest odd number.

### Consecutive Odd Numbers

The odd numbers comes just after a given odd number is called the **Consecutive Odd Number.**

Since there is a difference of 2 between two odd numbers, thus we can find as many consecutive odd numbers by adding 2 to an odd number.

**Example**

1, 3, 5, 7, 9, 11, . . . . . are the examples of some consecutive odd numbers.

### Odd Successor of an Odd Number

The odd number comes just after a given odd number is called the **Odd Successor** of that odd number.

#### Finding the odd successor of an odd number

Since, there is a difference of 2 between two consecutive odd numbers, thus we can get the odd successor of an odd number by adding 2 in it.

**Example**

(a) What is the odd successor of the odd number 3?

**Solution**

Since we can get an odd successor of a given odd number by adding 2 to it.

Thus, the odd successor of 3

= 3 + 2 = 5

Thus, 5 is the odd successor of the odd number 3.

(b) What is the odd successor of the odd number 5?

**Solution**

Since we can get an odd successor of a given odd number by adding 2 to it.

Thus, the odd successor of 5

= 5 + 2 = 7

Thus, 7 is the odd successor of the odd number 5.

(c) What is the odd successor of the odd number 11?

**Solution**

Since we can get an odd successor of a given odd number by adding 2 to it.

Thus, the odd successor of 11

= 11 + 2 = 13

Thus, 13 is the odd successor of the odd number 11.

(d) What is the odd successor of the odd number 13?

**Solution**

Since we can get an odd successor of a given odd number by adding 2 to it.

Thus, the odd successor of 13

= 13 + 2 = 15

Thus, 15 is the odd successor of the odd number 13.

(e) What is the odd successor of the odd number 95?

**Solution**

Since we can get an odd successor of a given odd number by adding 2 to it.

Thus, the odd successor of 95

= 95 + 2 = 97

Thus, 97 is the odd successor of the odd number 95.

### Odd Predecessor of an Odd Number

The odd number comes just before a given odd number is called the **Odd Predecessor** of that odd number.

#### Finding the odd predecessor of an odd number

Since, there is a difference of 2 between two consecutive odd numbers, thus we can get the odd predecessor of an odd number by subtracting 2 in it.

**Example**

(a) What is the odd predecessor of the odd number 13?

**Solution**

Since we can get an odd predecessor of a given odd number by subtracting 2 to it.

Thus, the odd predecessor of 13

= 13 – 2 = 11

Thus, 11 is the odd predecessor of the odd number 13.

(b) What is the odd predecessor of the odd number 15?

**Solution**

Since we can get an odd predecessor of a given odd number by subtracting 2 to it.

Thus, the odd predecessor of 15

= 15 – 2 = 13

Thus, 13 is the odd predecessor of the odd number 15.

(c) What is the odd predecessor of the odd number 51?

**Solution**

Since we can get an odd predecessor of a given odd number by subtracting 2 to it.

Thus, the odd predecessor of 51

= 51 – 2 = 49

Thus, 49 is the odd predecessor of the odd number 51.

(d) What is the odd predecessor of the odd number 67?

**Solution**

Since we can get an odd predecessor of a given odd number by subtracting 2 to it.

Thus, the odd predecessor of 67

= 67 – 2 = 65

Thus, 65 is the odd predecessor of the odd number 67.

(e) What is the odd predecessor of the odd number 71?

**Solution**

Since we can get an odd predecessor of a given odd number by subtracting 2 to it.

Thus, the odd predecessor of 71

= 71 – 2 = 69

Thus, 69 is the odd predecessor of the odd number 71.