### Prime and Composite Numbers

#### Prime Numbers

Let’s observe the factors of few natural numbers.

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: 19

19 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.

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: 15

15 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.

#### 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.

#### 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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