### Odd Numbers

**WHAT ARE NUMBERS?**

Numbers are the building blocks of mathematics. These can be used to count or measure something. It has a very important role in our daily life and mathematics**.**

The ten mathematical digits (0 to 9) are used to represent ages, weight, birthdays, time, scores, bank accounts, and telephone numbers. One cannot imagine their life without these ten numbers.

Numbers are of various types like Natural Numbers (N), Whole Number (W), Integer (Z), Rational Number (Q), Real Number (R), etc.

Natural Numbers, Whole Number and Integers can be further classified into odd numbers and even numbers.

Odd and even numbers have a major role in the foundation of learning many mathematics concepts. Understanding even and odd numbers is important in mastering some of the most difficult math concepts.

**WHAT ARE ****ODD NUMBERS?**

Odd numbers are the whole numbers which are not divisible by 2. If we divide an odd number by 2, then it will leave a remainder as 1. Odd numbers end with the digits 1, 3, 5, 7 or 9. Odd numbers are the opposite of even numbers. The odd numbers cannot be arranged in pairs. Odd numbers are not the multiples of 2.

The examples of odd numbers are 1, 3, 5, 7,31, 43 etc.

For example, 13 is not exactly divisible by 2 because it leaves 1 as remainder when we divide it by 2 and it ends with 3. So, 13 is an odd number.

**LIST OF ODD NUMBERS FROM 1 to 100:**

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49,51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99

**NOTE: **

- The smallest odd number is 1.
- There are 25 odd numbers from 1 to 50 while there are 50 in between 1 and 100.
- Every number coming after an even number is an odd number.
- Every number coming after an odd number is an even number.
- Fractions and Decimals are not even numbers or odd numbers, because they are not whole numbers.

**WHAT ARE EVEN NUMBERS?**

Even numbers are those numbers that are exactly divisible by 2. Even numbers always end up with the last digit as 0, 2, 4, 6, or 8. Any number divisible by 2 without leaving any remainder is called an even number.

Examples of even numbers are 24, 56, 88, 102, etc.

**What is Property?**

The property of an integer whether it is even or odd is called parity.

An integer's parity is even if it is divisible by two with no remainders left and its parity is odd if it is not divisible by 2 and its remainder is 1.

Any two consecutive integers have opposite parity.

Even and odd numbers have opposite parities.

For example, 15 is odd and 16 even has opposite parities

29 is odd and 14 even has opposite parities.

**GENERAL FORM OF ODD NUMBERS**

An odd number is an integer of form 2k+1, where k ∈ Z (i.e., integers) are called odd numbers.

If we put any value of k, we will get an odd number.

For example: If we take k as 2, will get 2 x 2 + 1 = 5, which is an odd number.

An even number is an integer of the form 2k, where k ∈ Z (i.e., integers) are called odd numbers.

If we put any value of k, we will get an even number.

For example: If we take k as 2, will get 2 x 2 = 4, which is an even number.

**HOW TO CHECK WHETHER A NUMBER IS EVEN OR ODD?**

There are two methods of identifying whether a number is even or odd. They are:

**1. By checking the digit of the number at the unit’s place:**

To check whether a number is an odd number or an even number, we have to check the number at “ones” or “units “place or the end digit of the number.

The numbers ending with the digits 1,3,5,7 and 9 are the odd numbers.

Example: 7,11,283,5735,9859 etc.

As the number 2835 ends with the digit 5 (odd number), the given number is an odd number.

And,

The numbers ending with the digits 0,2,4,6 and 8 are the even numbers.

As the number 2838 ends with the digit 8 (even number), the given number is an even number.

**2. By Grouping:**

Here we have a total of 11 dots. All the dots are not paired up. One dot is left unpaired. Such numbers that cannot be put into pairs are called **odd numbers.**

Those numbers which are not exactly divisible by 2 are called odd numbers.

Now,

There are 12 dots. We observe that all the dots are paired and no dot is left unpaired, so,12 is an even number.

We can conclude that all those numbers that can be put into pairs are called even numbers.

**PROPERTIES OF ODD** **NUMBERS**

**Property of Addition of two odd numbers**

- When we add two odd numbers the results are always even.

Example: 7(odd) + 5(odd) = 12 (even)

- When we add one odd number and one even the results are always odd.

Example: 9(odd) + 2(even) = 11(odd)

**Property of Subtraction of odd Numbers**

- When we subtract two odd numbers the results are always even.

Example: 9(odd) – 3(odd) = 6(even)

- When we subtract one odd number and one even the results are always odd.

Example: 15(odd) – 10(even) = 5(odd)

**Property of Multiplication of odd numbers**

1. When we multiply two odd numbers, the results are always odd.

Example: 3(odd) x 5(odd) = 15(odd)

2. When we multiply one odd number and one even number, the results are always even.

Example: 5(odd) x 2(even) = 10(even)

**Property of Division of odd numbers**

1. When we divide two odd numbers the result is an odd number, only when the denominator is a factor of the numerator.

Example: When we divide 15 by 5 and 5 is a factor of 15, we get 3, which is a whole number.

- When we divide two odd numbers and the denominator is not a factor of the numerator, so the result may be a fraction or decimal (terminating or non – terminating).

Example: when we divide 5 by 15, we get 1/3(fraction) or 0.3333(non – terminating decimal)

**TYPES OF ODD NUMBERS**

The numbers which are not the multiple of 2 are the odd numbers.

**Composite odd numbers**: Those composite numbers which cannot be divided by 2 are the composite odd numbers, and all the positive integers that have a factor other than 1 are known as composite numbers. These types of odd numbers are formed by the product of two smaller positive odd integers.

The list of composite odd numbers from 1 to 50 is as follows.

9, 15, 21, 25, 27, 33, 45, 49.

**Consecutive odd numbers**: Consecutive odd numbers are the odd numbers that follow each other in sequential order. They have a difference of 2 between them. If n is an odd number, then the numbers n and n+2 are consecutive odd numbers.

The consecutive odd numbers from 1 to 20 are:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19

**SUM OF ODD NUMBERS FROM 1 TO 1000**

According to the sum of odd numbers formula, the sum of first n odd numbers is given by n2 where n is a natural number and represents the number of terms.

Thus, the sum of first n odd numbers will be represented as 1 + 3 + 5 +...+ n terms = n2

**FUN FACTS:**

- When you add up all the odd numbers from 1 to any number, the sum will always be a perfect square.
- The sum of all the odd numbers from 1 to 100 is 2500 and the sum is a perfect square.
- Even numbers create symmetry, but odd numbers create interest and are easier to remember
- Some superstitious people believe that even numbers are unlucky. Part of it is because they are divisible, which lessens or reduces their power. Odd numbers are more powerful because they cannot be reduced like this.

### Videos (3)

### Examples

## Q1 .Find the odd numbers between 13 and 20

## Solution:

The odd numbers between 13 and 20 are 15, 17 and 19.

## Q2. Check whether 18984 is even or odd.

## Solution:

As 18984 ends with 4, which is an even number.

So, 18984 is an even number.

## Q3.Check whether 9957 is even or odd.

## Solution:

As 9957 ends with 7, which is an odd number.

So, 9957 is an odd number.

### Practice Questions

## Odd Numbers Practice Questions

### Related Study Materials

### FAQ

### What is an odd number?

The numbers which are not divisible by 2 are called an odd numbers. The odd number ends with the digits 1,3.5,7 and 9. Some examples of odd numbers are 123,515,11 etc.

### What are the two types of odd numbers?

The two types of odd numbers are:

- Composite odd numbers
- Consecutive odd numbers

### What are the properties of odd numbers?

The properties of odd numbers are:

- Odd numbers end with the digits 1, 3, 5, 7, or 9.
- If we divide an odd number by 2, then it will leave a remainder as 1.
- Odd numbers are the opposite of even numbers.
- The odd numbers cannot be arranged in pairs.
- Odd numbers are not the multiples of 2.

### What is the smallest odd number?

The smallest odd numbers is ‘1’.

### What is the general form of odd number?

The general form of odd number is 2k+1, where k ∈ Z (Z are integers)

### What is the difference between odd numbers and even number?

Odd numbers are the whole numbers which are not divisible by 2 and Even numbers are the numbers which are divisible by 2.

Odd numbers end with 1, 3, 5, 7 or 9 and even numbers end with 0, 2, 4, 6 and 8.

### How will you check whether the given number is odd or even?

If the number ends with 1,3,5,7 and 9, then the number is called an odd number.

If the number ends with 0,2,4,6 and 8 then the number

is called an even number

### Is 0 an odd number?

No, zero is not an odd number because when odd numbers are divided by 2 then 1 is left behind, as the remainder, but if we divide 0 by 2 then the result is 0.

### Is 67 odd or even number?

67 is an odd number as the digit at unit’s place is 7, which is an odd number.

### What is the sum of two odd numbers?

The sum of two odd numbers is always even.

### What is the difference of two odd numbers?

The difference of two odd numbers is always even.

### How many odd numbers and even numbers between 1 to 1000?

There are 500 odd numbers and 500 even numbers between 1 to 1000

Acute Angled Triangle | Right Angled Triangle | Obtuse Angled Triangle |

### Videos(3)

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