### Playing With Numbers - Prime and Composite Numbers

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#### Prime Numbers

Let’s observe the factors of few natural numbers.

Numbers

Factors

Number of Factors

1

1

1

2

1, 2

2

3

1, 3

2

4

1, 2, 4

3

5

1, 2

2

6

1, 2, 3, 6

4

We can see that number 1 has only one factor (i.e. itself).There are numbers that have exactly two factors i.e.1 and the number itself. Such numbers are 2, 3, 5, etc. These numbers are

__prime numbers__. A number is called prime when it can't be divided evenly by any number except 1 or itself.#### Therefore, Prime numbers are natural numbers that have only 2 factors i.e. 1 and itself.

__Example:__1919 have only two factors, 1 and 19. 19 cannot be divided evenly by numbers other than 1 or itself. So, 19 is a prime number.

#### Co – Prime Numbers

#### The two numbers are said to be co-prime numbers when there is no number, other than 1, that divides both the two given number evenly. The HCF of these numbers should be 1.

__Example:__6 and 35 are co-prime#### Composite Numbers

Let’s observe factors of natural numbers again.

Numbers

Factors

Number of Factors

1

1

1

2

1, 2

2

3

1, 3

2

4

1, 2, 4

3

5

1, 2

2

6

1, 2, 3, 6

4

There are numbers having more than two factors like 4, 6, etc. These numbers are composite numbers. When a number can be divided up evenly it is a Composite Number. A composite number has factors in addition to one and itself.

#### Therefore, numbers having more than two factors are called Composite numbers.

__Example__: 1515 have three factors, 1, 5 and 15. 15 can be divided evenly by numbers other than 1 or itself. So, 15 is a composite number.

**Prime and Composite Number Chart (1 to 100)**#### 1. 1 is neither a prime nor a composite number.

#### 2. All the numbers in orange box are prime numbers. All the numbers in white box, other than 1 are composite numbers.

**Important Notes:**#### 1. The numbers 0 and 1 are neither prime nor composite.

#### 2. Every prime number except 2 is odd.

#### 3. HCF of two prime numbers is always 1

#### 4. Even numbers are divisible by two and so all even numbers greater than two are composite numbers.

__Example:__2, 4, 6, 8, 10#### 5. 1 is co-prime with every number.

#### 6. Every prime number is co-prime to each other.

__Example:__3 and 5#### 7. Any two successive numbers are always co-primes.

#### 8. The sum two prime numbers can be even or odd.

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