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All numbers are categorised as one or the other prime or composite, with the exemptions of zero and one, which are extraordinary cases. We should investigate the difference between prime and composite numbers. Prime numbers have precisely two elements, one and the actual number. On the off chance that you realise your divisibility rules deciding the prime numbers from 1-to 100 is a generally simple errand. Here are the prime numbers up to 25:
2, 3, 5, 7, 11, 13, 17, 19, 23.
In this article, we will see whether 2 is a prime or composite number and what is a co-prime number.
What is a Prime Number?
The numbers which have only two factors are known to be prime numbers. Examples of prime numbers are three, five, seven, eleven, thirteen, etc. These numbers have only two factors, i.e., one and the number itself. For example, one factor is one for the number three, and another is the number three itself.
Prime numbers between 1 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
One is not a prime number because it has no other factors than one itself.
What is a co-prime number?
When the only common factor of two numbers (a,b) is one, then the numbers are termed Co-prime Numbers.
They are also termed Relatively prime or Mutually Prime Numbers.
For example {4,7}, {3,8}, {9,22}.
Why 2 is not a prime number or a composite number?
For a number to be considered a Prime number, it has to have only two factors:- 1 and the number itself.
This condition is fulfilled by 2; hence two is a Prime Number.
For a number to be a Composite Number, it has to have more than two factors as its divisor:- factors of 6 are – (1, 2, 3, 6); therefore, 6 is a composite number.
This condition is not fulfilled by 2; hence 2 is not a Composite number.
Therefore from the above analysis, we can say that two is a Prime Number but not a Composite number.
Properties of Co- prime Numbers
Co-prime numbers can be distinguished effectively with the assistance of certain properties that are made sense of beneath:
The Highest Common Factor (HCF) of two coprime numbers is one. For instance, 5 and 9 are coprime numbers, HCF (5, 9) = 1.
The Least Common Multiple (LCM) of two coprime is generally their item. For instance, 5 and 9 are co-prime numbers. Consequently, LCM (5, 9) = 45.
One forms a co-prime number pair with each number.
Two even numbers can’t be co-prime numbers as they generally have two as the normal element.
The amount of two coprime numbers are generally coprime with their item. For instance, 5 and 9 are co-prime numbers. Here, 5 + 9 = 14 is coprime with 5 × 9 = 45.
Two prime numbers are coprime all of the time. They have just one as their normal component. Think about 29 and 31. 29 has two prime elements, 1 and 29 in particular. 31 has two prime variables, 1 and 31, as it were. 29 and 31 are prime numbers. They have just a single normal element 1.
Hence they are co-prime. We can look at any two prime numbers and get them as coprime. For instance, 2 and 3, 5 and 7, 11 and 13, etc.
All sets of two consecutive numbers are co-prime numbers. Any two back to back numbers have one as their normal variable.
Difference between Co prime and twin prime
Co-prime and Twin Prime Numbers
The numbers whose HCF are Co-prime numbers. Then again, the prime numbers whose difference is always two are called Twin prime numbers. For instance, 9 and 7 are twin prime numbers. The accompanying focuses list the distinction between co-prime and twin prime numbers. Twin prime numbers are generally prime numbers, while coprime numbers can be composite numbers too.
The distinction between two twin primes is generally two, while the contrast between two co-primes can be any number.
{11,13} twin prime
{3,8} co-prime
Every one of the sets of twin prime numbers can be termed a co-prime, which may not be the same as co-primes, as all the co-primes can not be twin primes. One forms a coprime pair with each number, while it forms a twin pair with 3.
Handy notes for aspirants
Any numbers that are consecutive {4,5} are Co prime numbers.
Even numbers can never be termed as Co prime
2 prime numbers {3,11} can be coprime
The versatility of 1 is that it can form co-prime with any number.
A number can be a prime number and a co-prime number with another number that is not multiple.{ 3,17}
Conclusion
Numbers having exactly two factors are called prime numbers, whereas numbers having more than two factors are called Composite. Zero and one are neither categorised as Prime or Composite numbers. The Divisibility test is the easy way to determine the factors of any whole natural number. Every composite number can be written as a unique product of prime numbers, called a number’s prime factorisation. We hope that this article has helped with the conceptual study of what is a prime number, what is a co-prime number and whether two is a prime or a composite number.
