Prime Numbers and Composite Numbers Relation

Numbers are generally classified into 2 types: prime numbers and composite numbers. The main difference between these 2 is the factors of the number. The definition of prime and composite numbers is that prime numbers have only 2 factors and composite numbers have more than 2 factors. The numbers can also be classified as coprime numbers. Coprime numbers are the numbers that have exactly 1 number as a common factor. The prime number and the composite number is generally regarded as natural number. The prime number is generally greater than 1 and is not a product of any 2 natural numbers. Any number which is greater than 1 and is not a prime number is regarded as a composite number.

Definition of Prime and Composite Numbers

A prime number is defined as a number that has only 2 factors, out of these two factors one factor is the number 1. Any 2 prime numbers having at least 1 common factor are known as coprime numbers. For example, numbers like 3,5,7,11 are prime numbers as their factors are 1 and the number itself.

A composite number is defined as a number that has more than 2 factors, meaning it can be divided by 1, the number itself, and also by some other number. For example, the number 14; its factors are 1,7,14.

Facts About Prime Numbers

• The only even prime number in the number system is the number 2. As 2 cannot be further divided into its factors but is capable of becoming the factor of that is it can divide all even numbers in the number system
• Few numbers even after following the property of a prime number are not considered a prime number, for example, 0 and 1
• The numbers 0 and 1 for a change do not even fall under the category of composite numbers
• There is no prime number greater than 5 that ends with 5, as any number which ends with 5 can simply be divided by 5

Facts About the Composite Number

• Composite numbers have more than 2 factors
• They are evenly divisible by their factors and also by other composite numbers
• The smallest composite number known is 4
• Each composite number is known to include at least 2 prime numbers as its factors
• Composite numbers are further divided into 2 types; odd composite numbers and even composite numbers

Types of Composite Number

Composite numbers are categorized into 2 types as follows;

• Odd composite numbers- odd numbers which do not fall under the category of prime numbers are regarded as odd composite numbers, like 21,45, and many more. Exceptions to this are 1,3,5,7 these numbers are odd but are not odd composite numbers
• Even composite numbers- even numbers that are not a prime number are regarded as even composite numbers like 4,6,8, and many more

Ways to Find if a Number is Prime or Composite

There are 2 methods of determining whether a number is a prime or a composite number;

• Divisibility method- we can check the number for prime or composite by performing the divisibility test in orders 2,3,5,7,11,13, and 17. Let us consider a number less than 121 and it is not divisible by 2,3,5, or 7, then it would be a prime number otherwise it is regarded as a composite number. If a number is less than 289 and is not divisible by 2,3,5,7,11, or 13, then the number would be a prime number otherwise it would be a composite number
• Prime factorization method- this method is used to find the prime factors of a composite number. In this method, the number is divided by prime numbers to a point where no reminder is left behind and the prime numbers which divide the composite number are regarded as the factors of that number. If prime factorization of a prime number is done then the factors come out to be 1 and the number itself which helps us to identify a prime number

Conclusion

There are 2 types of numbers, one is a prime number and the other is a composite number. The definition of prime and composite numbers is that prime numbers have only 2 factors and composite numbers have more than 2 factors. Apart from these 2 types, there is another type of number known as coprime numbers that have exactly 1 number as a common factor. Both the numbers differ from each other only in 1 thing; the number of factors they have. Some numbers are also an exception to this classification like 0 and 1, both these numbers are not regarded as prime or composite numbers. Composite numbers are further divided into 2 types; odd composite numbers and even composite numbers. The prime and composite numbers can be differentiated with the help of the prime factorization method and divisibility test.