Natural number can be defined as a set of whole numbers that can be used for counting. Natural numbers is the set of positive number. Natural numbers can be divided into different groups according to different properties. When we consider the factor of a number, the set of natural number can be divided into two sets, prime numbers, composite numbers. Natural numbers greater than 1 that are not prime are called composite.

A** prime number** is a natural number greater than 1 that has no positive
divisors other than 1 and itself. A natural number greater than 1 that
is not a prime number is called a **composite number**

A

Factors of 2 are 1 and 2.

=> Yes, 2 is prime number.

=> Yes, 2 is prime number.

Given number = 32

Factors of 32 = 1, 2, 4, 8 and 32

=> A Prime Number can be divided evenly only by 1 or itself.

=> 32 is not a prime number.

Factors of 32 = 1, 2, 4, 8 and 32

=> A Prime Number can be divided evenly only by 1 or itself.

=> 32 is not a prime number.

Number = 6

=> Factors of 6 = 1, 2, 3 and 6.

=> 6 have more than two factors

=>**6 is a composite number.**

=> Factors of 6 = 1, 2, 3 and 6.

=> 6 have more than two factors

=>

Number = 35

Factor of 35 = 1, 5, 7 and 35

=> 35 have more than two factors.

=>**35 is a composite number.**

Factor of 35 = 1, 5, 7 and 35

=> 35 have more than two factors.

=>

Natural numbers are classified as prime numbers, composite numbers and number neither prime nor composite:

In the set of numbers from 1 to 20,

- 1 is neither prime nor composite.
- 2, 3, 5, 7, 11, 13, 17, and 19 are prime numbers.
- 4, 6, 8, 9, 10, 12, 14, 16, 18, and 20 are composite numbers.

=> Factor of 1 = 1.

But according to the definition of prime, a number can only have 1 and it self as a factors.

=>

According to the definition of composite number, a number can have more factors other than 1 and the number itself.

=> For 1, the factors are 1 and the number 1 itself.

=> Factor of 1 = 1.

=>

From (1) and (2), we conclude that 1 is neither prime nor composite

One is the only natural number which is neither prime nor composite.

Number = 27

Factors of 27 = 1, 3, 9 and 27

=> Factors of 27 are more than two.

=>**27 is a composite number.**

Factors of 27 = 1, 3, 9 and 27

=> Factors of 27 are more than two.

=>

Number = 43

Factors of 43 = 1 and 43

=> Factors of 43 are 1 and number itself, so according to the definition of prime number, 43 is a prime number.

=>** 43 is a prime number.**

Factors of 43 = 1 and 43

=> Factors of 43 are 1 and number itself, so according to the definition of prime number, 43 is a prime number.

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