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Prime Numbers And Composite Numbers: Know Their Differences

Prime numbers and composite numbers are two different and important concepts in Mathematics. It is the foundation to understand the subject ‘Mathematics’ in depth. The number of factors determines whether it is a prime number or a composite number. 

In this article, we have briefed out simple definitions of prime numbers and composite numbers, the difference Between Prime Numbers and composite numbers, their types, and how to check whether a number is a prime number or a composite number. 

Prime Numbers

Prime numbers are defined as the numbers that are divisible by 1, and the numbers themselves are known as prime numbers. Prime numbers only have two factors. 

  • Examples of Prime Numbers:

2, 3, 5, 7, 11, 13, and so forth are examples of prime numbers.

How they are known as prime numbers; let’s check:

  • 2: The number 2 is divisible by the number 1 and by itself, i.e. 2.
  • 3: The number 3 is divisible by the number 1 and by itself, i.e. 3.
  • 5: The number 5 is divisible by the number 1 and by itself, i.e. 5.

In the above examples, the numbers had only two factors. Even though number 1 is divisible by itself, it is not a prime number. A prime number should and must have exactly two factors. 

The factors shouldn’t be less than two or more than two. However, numbers such as 4, 6, 9, etc., are also divisible by 1 but are not called prime numbers since they are divisible by more than two numbers and have more than two factors.

  • 4: The number 4 is divisible by 1, 2, and 4.
  • 6: The number 6 is divisible by 1, 2, 3, and 6.
  • 9: The number 9 is divisible by 1, 3, and 9.

In the above examples, the numbers had more than two factors. Hence, they are not prime numbers.

Composite Numbers

If you understand what prime numbers are, it is not difficult to understand the composite numbers. The numbers which are not known as prime numbers are known as composite numbers. (Except for the number 1). The composite numbers have more than two factors. In other words, the numbers divisible by more than two numbers are known as composite numbers.

  • Examples of Composite Numbers:

4, 6, 9, 10, 12, and so forth are the examples of composite numbers

How to check them as composite numbers:

  • 4: The number 4 is divisible by the numbers 1, 2, and 4.
  • 10: The number 10 is divisible by the numbers 1, 2, 5, and 10.
  • 12:The number 12 is divisible by 1, 2, 3, 4, 6, and 12.

In the above examples, all the numbers had more than two divisible factors. Hence, they are composite numbers.

While verifying whether a number is a prime or composite number, always start with the “factor 1”.

 

Important Points To Remember

  1. Number 1 is not either a prime number or a composite number. (Since it has only one factor and it fails to satisfy both the definitions).
  2. Prime numbers are infinite in the count, and all the prime numbers are odd numbers except for the number ‘2’.
  3. Both prime and composite numbers are natural numbers (Natural numbers start from 1 till infinite and only include positive integers). 
  4. Zero doesn’t come under a prime number or a composite number. 
  5. Negative numbers cannot be prime numbers or composite numbers. In other words, negative integers are not included in the definition of prime or composite numbers. 
  6. Not every non-prime number is known as a composite number. Example: “number 1”.
  7. Both prime and composite numbers are whole numbers because the numbers are greater than 1. 
  8. Except for the numbers 0 and 1, all the numbers are either prime numbers or composite numbers.

Types of Prime Numbers

Even prime numbers, odd prime numbers, and twin prime numbers are the three types: 

  1. Even Prime Numbers: In all the even prime numbers, the only even prime number is 2. It is also known as a unique prime number. 
  2. Odd Prime Numbers: Prime numbers other than 2 are known as odd prime numbers. 5,7,11,13,17,19…etc are odd prime numbers. 
  3. Twin Prime Numbers: Twin prime or prime twin or prime pair are those prime numbers that have 2 as the difference between two prime numbers.

Example: 3 and 5 are prime numbers, and they have exactly 2 as the difference between them.

(3,5), (5,7), (11,13), etc., are examples of the twin prime numbers.

Types of Composite Numbers

Even composite numbers and odd composite numbers are the types. 

  1. Even Composite Numbers: All those numbers that are not prime numbers and are even are known as ” even composite numbers.”

Examples: 4, 6, 8, 10, 12, 14, 16, etc are even composite numbers.

  1. Odd Composite Numbers: All those numbers that are not prime and odd are known as odd composite numbers.

Examples: 9, 15, 21, 25, 27, 49, etc are odd composite numbers.

Difference Between Prime Numbers And Composite Numbers

  1. Prime numbers can be broken down into two factors: the number itself and 1, whereas composite numbers can be broken down into more than two factors. 
  2. Prime numbers factors cannot be expressed without the number 1, whereas composite numbers factors can be expressed without the “number 1.”

Practice Problems

  1. Is 12 a prime number or a composite number?

First, let us find the factors of 12. If the factors are more than two, we can conclude a composite number without verifying under prime numbers.

Factors of 12: 

  • 12 = 4×3
  • 12 = 2×6

Since the number 12 has more than two factors, i.e., 4, 3, 2, and 6, the number is composite.

  1. Find whether 13 is a composite number or a prime number

Let us first find the factors of 13 (i.e. the numbers are multiplied by 13)

Since 13 = 13×1,

the only factors are 13 and 1.

13 only has two exact factors. Therefore the number 13 is a prime number.

  1. Find whether the number 15 is a prime number or a composite number

Let us first write down the factors of 15:

  • 15 = 15×1
  • 15 = 3×5

Therefore the factors are 15, 1, 3, and 5. Since it has more than two factors, 15 is a composite number.

 

 

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