Real Numbers

Consider the following set of numbers.

2, 3, 5, 7, 11, 13, 17, 19…

Is there any similarity between these numbers?

Each number in the above set of numbers is divisible by 1 and the number itself, or we can say that each number in the above set has only two divisors i.e., 1 and the number itself. Such numbers are called **prime numbers.**

Let us learn more about prime numbers.

A prime number can be written as a product of only two factors. These factors are called **prime factors.**

For example, 23 = 1 × 23

Hence, 1 and 23 are the prime factors of 23.

There are two kinds of prime numbers.

(1) Even prime numbers

(2) Odd prime numbers

Prime numbers which are divisible by 2 are known as **even prime numbers **and those which are not divisible by 2 are known as **odd prime numbers.**

Examples of odd prime numbers are 3, 5, 7 etc .

It is to be **noted** that 2 is the only even prime number.

Now, consider the numbers other than 1 and prime numbers as follows:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18…

All these numbers have more than two divisors. Such numbers are called **composite numbers**.

Like prime numbers, composite numbers are also of two types.

(1) Even composite numbers

(2) Odd composite numbers

Composite numbers which are divisible by 2 are **even composite numbers** and those which are not divisible by 2 are **odd composite numbers.**

For example, 6, 24, 36, 42, etc. are even composite numbers while 9, 25, 39, etc. are odd composite numbers.

Let us go through the following video to have a better understanding about prime and composite numbers.

Note that** **3 is the smallest odd prime number.

**Twin primes:**

If a pair of prime numbers is such that the difference between those numbers is 2 then such prime numbers are known as **twin primes** and the pair is called **twin prime pair**.

For example, the numbers 3 and 5, both are prime numbers and the difference between them is 2, so these are twin primes and make a twi…

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