Counting Numbers

Counting numbers are sets of numbers that we use to learn how to count. They are for counting and measuring in our everyday life e.g the quantity of salt to be used for cooking, the quantity of sugar to be used in tea, and the speedometer of a vehicle. 

Examples of Counting Numbers: 

1. Natural Numbers 
2. Prime Numbers 
3. Even Numbers 
4. Odd Numbers 

1. Natural  Numbers: These are whole numbers greater than zero e.g 1, 2, 3, 4, 5, 6, 7 … 

2. Prime Numbers: These are natural numbers which have no factor other than 1 and themselves. In other words, they can be divided only by themselves or 1, e.g 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 ….

Note:
1 is not a prime number because it has only one factor, namely 1. Prime numbers need to have exactly two factors.

3. Even Numbers: The set of all-natural number which is divisible by 2. It is denoted by E. where E = {2, 4, 6, 8, 10, ………\( \scriptsize \infty \)}

4. Odd Numbers: The set of all natural numbers which are not divisible by 2 are called odd numbers, in other words, the natural numbers which are not even numbers are odd numbers. It is denoted by O. i.e. O = {1, 3, 5, 7 …. \( \scriptsize \infty \)}

Note:
\( \scriptsize \infty \)means infinity. Infinity is the idea of something that has no end. 

Worked Example 1.3.1:

Write down all natural numbers between 30 and 40. 

Solution  

31, 32, 33, 34, 35, 36, 37, 38, 39. 

Note:
30 and 40 are not inclusive because the question says “between” 30 and 40. 

Worked Example 1.3.2:

Write all the prime numbers from 11 to 31. 

Solution 

11, 13, 17, 19, 23, 29, 31 

Note:
11 and 31 are included because the question says “from” 11 to 31

Worked Example 1.3.3:

List all the odd numbers between 50 and 70. 

Solution 

50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Ans = 51, 53, 55, 57, 59, 61, 63, 65, 67, 69.

Worked Example 1.3.4:

List the first five even numbers from 110.  

Solution

110 111 112 113 114 115 116 117 118

Ans = 110, 112, 114, 116, 118.