Co-Primes (or Relative Prime)

In quantitative aptitude, a co-prime number can be said to be those pairs that have no common factor. The only common factor that they have is 1. For there to be a set, there have to be two numbers. Composite numbers like 4 as well 9 are co-prime. Co prime numbers are also called prime numbers, mutual or relative prime. GCF or Greatest Common Factor is the method used for finding out what two numbers are the co-prime numbers. HCF or as it is known as the highest common factor is 1 always for co-prime numbers. 

Co prime Number

Co prime numbers can be said to be those pairs that have no common factor. The only common factor that they have is 1. For there to be a set, there have to be two numbers. 

Here is a list of coprime numbers:

• 2,3
• 3,5
• 4,9
• 5,7
• 11,13

What is a co-prime number?

A co-prime number can be defined as those pairs that have no common factor. The only common factor that they have is 1. For there to be a set, there have to be two numbers. (4, 7) and (5,9) are co-prime number examples. Integers which are a and b are coprime on the condition that their divisor is 1. The GCD or Greatest Common Divisor is said to be 1. Fractions of co-prime number sets are going to be co-prime numbers as well. The only exceptions are 14 and 25. These numbers are not individually considered co-prime but when they are taken together, their divider is common which is 1. 

Notation 

Notation can be represented as:

• Gcd (a, b)=1
• (a, b) =1

Properties of Co-prime

Here are certain properties of co-prime number

• 1 is universal co-prime
• Consecutive numbers that are integers will be coprime given their HCF=1
• Two prime numbers will always be coprime
• Even numbers can’t be coprime
• 0 as well 5 together are not considered to be co-prime

Coprimality Probability

Coprimality Probability is a principle upon which the likelihood of two numbers being coprime can be understood and seen. It is a method of determinism that if integers are chosen randomly then how likely are they to be co-prime numbers. In arithmetic, there is a theorem based on this. That theorem is called Fundamental Theorem. In this case, co-primes are represented as a and b when no other prime number divides them. Setwise coprime occurs when there is a set of revolving integers. For example, (a1, a2…an). When all the integers that are involved in the set are coprime then those are called pairwise coprime. Infinite integers set can also be coprime pairwise. That will be determined based on the Sylvester sequence. Fermat numbers are also taken into account. 

Examples of Coprime

Table 1 shows examples of coprime numbers

Application of Coprime

Co prime numbers can be applied in various geometric, arithmetic, mathematics, and adjacent fields due to their versatility. The simple nature of co-prime numbers makes it very easy for them to be applied in geometry and arithmetic. Oftentimes it is also useful for higher standards of arithmetic. It is an important part of qualitative aptitude as well. Calculations based on coprime and identifying the correct co-prime can come in the examination. 

• Geometry- Calculating the side of a square or a tile is a situation where co-prime as a method can be applied. Through that, it can be figured out that square sides if they are co-prime then it cannot be covered. 
• It can also be used in the field of mechanical gears. While studying engineering as well as preparing for certain aspects of banking examinations, co-prime can be applied. 

Conclusion

Therefore, it is of no surprise that co-prime is so widely used in geometry. It is an interesting element of mathematics providing many interesting facets. In the article, Coprimality Probability has been discussed. The applications of co-prime have also been discussed. What are co-prime numbers have also been understood through relevant examples. It is an important part of qualitative aptitude as well. Calculations based on coprime and identifying the correct  co-prime  can come in the examination.