How can you tell if a pair of numbers are relatively prime or not?

When you want to know how prime numbers can be called relative primes. Then, there must be a question arising in your mind. What are twin prime numbers? So, as is clear from the name relative or twin primes, it means something consisting of two matching or corresponding parts. Thus, twin prime numbers are the prime numbers that have only one as the common factor, and their difference is equal to 2. Also, when we divide these numbers, we will get 0 as a reminder. Moreover, you can say Twin prime numbers as twin cousins. 

What is the relative prime number? 

The prime numbers whose common factor is one are called relative prime numbers. No number other than one can divide them. Moreover, when the gap between two relatively prime numbers is two. The number will be twin prime numbers. 

For example, 3 and 5 are prime numbers. They have only one common factor. So, it is relatively prime. And The difference between 3 and 5 is two. Thus, it is also twin primes. 

Properties of relative prime 

Here we are going to discuss some properties of relative prime. 

  1.It should be noted, the Highest Common Factor(HCF) of a relative or twin primes is always 1.Such as, 5 and 7 are prime numbers, and their common factor is 1.

2. The least common factor (LCM) of a relative prime number is equal to the product of these two numbers. Proof of this, 3 and 5 are relatively prime. And LCM of 3 and 5 is 15. Also, the product of 3 and 5 is 15.
3. When we add two relatively prime numbers, the results will always be the relative prime of their products. For example, when we add 3 and 5, the answers will be eight, and when we multiply 3 and 5, the answer will be 15. Hence, 8 and 15 are relatively prime. The only common factor of 8 and 15 is 1. It should be noted; it is not twin primes because the difference between 8 and 15 is not 2.

4. You will find any two prime numbers as relative prime but not twin prime numbers. 
5. The consecutive prime numbers will always be relative prime and twin primes. Proof of this, 7 and 9 are consecutive numbers. Their common factor is 1, so it is relatively prime. Also, the difference between these two is 2. So, it is twin prime numbers. 
6. Undoubtedly, two even numbers will not be relatively prime numbers. Because 2 is a common factor of even numbers. 

But one even and one odd number can be relatively prime numbers. 

For example, 4 and 7 are relatively prime numbers because the common factor is 1.

Steps to find relative prime numbers

If you want to find a pair of two numbers, is the reactive prime or not. Then, you will have to find the HCF of the two numbers. If you find the HCF of those numbers is 1, it will be a relative prime number. You can find the HCF of any number by listing their all factors. 

To clarify, we take the example of two prime numbers, 5 and 7. First, we list the factors of this. 

Factor 5 is 1 and 5.

Factor 7 is 1 and 7.

Thus, 1 is only a common factor of 5 and 7. So, it is relatively prime. 

Additionally, the difference between 5 and 7 is 2. So, it is twin prime numbers. 

Furthermore, We take the example of 6 and 9. First, we list the factors of this. 

Factor 6 is 1, 2, 3 and 6.

Factor 9 is 1, 3 and 9.

Thus, 1 and 3 are the common factors of 6 and 9. So, it is not relatively prime. Moreover, they are not twin prime numbers. 

Conclusion

After reading the above article, we get the title’s answer, how we can say a pair of numbers are relatively prime or not. Briefly, when a pair of numbers has no other factor than 1. We can say it is relatively prime numbers. In simple words, two numbers are called relatively prime when no number other than one can divide both of them. That means the greatest common divisor of these two numbers is one. Apart from this, the gap between two relatively prime numbers is 2. We can say it is twin prime numbers or twin cousins. Hence, we must clearly understand prime numbers, co-prime numbers, and composite numbers to get the point easily.