## Prime and Composite Numbers

Numbers can be divided on the basis of their factors in two categories, these categories are **Prime Numbers** and **Composite Numbers**.

### Prime Numbers

Numbers which have only two factors, 1 and the number themselves are called the **Prime Numbers**. **Examples**: The number 2 (two) has only two factors, 1 and 2, so 2 (two) is a **prime number**. The number 3 (three) has only two factors, 1 and 3, so 3 (three) is a **prime number**. The number 5 (five) has only two factors, 1 and 5, so 5 (five) is a **prime number**. The number 7 (seven) has only two factors, 1 and 7, so 7 (seven) is a **prime number**.

### Composite Numbers

Numbers which more than two factors are known as **Composite Numbers.** **Examples**: 4 has three factors, 1, 2, and 4, so 4 (four) is a **composite number**. 6 (Six) has four factors, 1, 2, 3, and 6, so 6 (six) is a **composite number**. Similarly, 8 (eight) has four factors, 1, 2, 4, 8, so 8 (eight) is a **composite number**.

## Eratosthenes Method: **The Sieve of Eratosthenes** to Find the Prime Numbers

Eratosthenes was a Greek Mathematician in the third BC. He proposed a method called ** The Sieve of Eratosthenes ** to find the Prime Numbers. Apart from this he gave many precious contributions, some of them are calculating the Circumference of the Earth, Calculate the Earth's axial tilt, proposed the parallels and meridians, etc.

### Finding the Prime Numbers between 1 and 100

Method to find the Prime Numbers between 1 and 100:

(a) Write all the numbers from 1 to 100 in a table format.

(b) Strike out the number 1, because 1 is not considered a prime number.

(c) Strike out all the numbers except 2, which are perfectly divisible by 2.

(d) Strike out all the numbers except 3, which are perfectly divisible by 3.

(e) Strike out all the numbers except 5, which are perfectly divisible by 5.

**Sieve of Eratosthenes**

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

26 27 28 29 30

31 32 33 34 35

36 37 38 39 40

41 42 43 44 45

46 47 48 49 50

51 52 53 54 55

56 57 58 59 60

61 62 63 64 65

66 67 68 69 70

71 72 73 74 75

76 77 78 79 80

81 82 83 84 85

86 87 88 89 90

91 92 93 94 95

96 97 98 99 100

Now make a list of numbers left. These numbers are **Prime Numbers** which have only two factors either 1 or number themselves.

### The list of **Prime Numbers** between 1 to 100 is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

*There are twenty five prime numbers between 1 to 100.*

This method of finding the **Prime Numbers** is called **The Sieve of Eratosthenes**.