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Coprime Numbers
Coprime numbers are pairs of numbers that do not have any common factor other than 1. There should be a minimum of two numbers to form a set of coprime numbers. Such numbers have only 1 as their highest common factor, for example, (4 and 7), (5, 7, 9) are coprime numbers. It is to be noted that coprime numbers need not be prime numbers always. Two composite numbers like 4 and 9 also form a pair of coprimes.
1.  What are Coprime Numbers? 
2.  How to Find Coprime Numbers? 
3.  Properties of Coprime Numbers 
4.  Coprime and Twin Prime Numbers 
5.  Coprime Numbers 1 to 100 
6.  FAQs on Coprime Numbers 
What are Coprime Numbers?
If the only common factor of two numbers a and b is 1, then a and b are coprime numbers. In this case, (a, b) is said to be a coprime pair. Coprime numbers are also referred to as relatively prime numbers.
Coprime Number Definition
The coprime number definition tells us that if the Greatest Common Factor (GCF) of any two numbers is 1, then they are said to be coprime.
Coprime Number List
Given below is the list of a few coprimes for your reference.
Pairs of Coprime Numbers 
(2,15) 
(3,8) 
(4,9) 
(5,6) 
(11,14) 
(15,19) 
How to Find Coprime Numbers?
To find whether any two numbers are coprime, we first find their Greatest Common Factor (GCF). If their GCF is 1, we can say that they are coprime.
Example 1: Let us consider two numbers 5 and 9. The factors of 5 are 1 and 5. The factors of 9 are 1, 3, and 9. The factor that is common to both 5 and 9 is 1. GCF of (5, 9) = 1. Thus, (5, 9) is a coprime pair.
Example 2: Let us consider two numbers 6 and 10. The factors 6 are 1, 2, 3, and 6. The factors of 10 are 1, 2, 5, and 10. Factors that are common to both 6 and 10 are 1 and 2. So GCF (6, 10) = 2. Thus, (6, 10) is NOT a coprime pair.
Properties of Coprime Numbers
Coprime numbers can be identified easily with the help of some properties that are explained below:
 The Highest Common Factor (HCF) of two coprime numbers is always 1. For example, 5 and 9 are coprime numbers, there, HCF (5, 9) = 1.
 The Least Common Multiple (LCM) of two coprimes is always their product. For example, 5 and 9 are coprime numbers. Hence, LCM (5, 9) = 45.
 1 forms a coprime number pair with every number.
 Two even numbers cannot be coprime numbers as they always have 2 as the common factor.
 The sum of two coprime numbers is always coprime with their product. For example, 5 and 9 are coprime numbers. Here, 5 + 9 = 14 is coprime with 5 × 9 = 45.
 Two prime numbers are always coprime. They have only 1 as their common factor. Consider 29 and 31. 29 has 2 prime factors, 1 and 29 only. 31 has 2 prime factors, 1 and 31 only. 29 and 31 are prime numbers. They have only one common factor 1. Thus they are coprime. We can check any two prime numbers and get them as coprime. For example, 2 and 3, 5 and 7, 11 and 13, and so on.
 All pairs of two consecutive numbers are coprime numbers. Any two consecutive numbers have 1 as their common factor.
Consider a few pairs of such numbers. Let us try with 14 and 15.
Numbers  14  15 
Factors  1,2,7,14  1,3,5,15 
Common Factor  1 
There are multiple such combinations where 1 is the only common factor.
Coprime and Twin Prime Numbers
Coprime numbers are those numbers whose HCF is 1. On the other hand, twin prime numbers are those prime numbers whose difference is always 2. For example, 3 and 5 are twin prime numbers. The following points list the difference between coprime and twin prime numbers.
 Twin prime numbers are always prime numbers while coprime numbers can be composite numbers as well.
 The difference between two twin primes is always 2 while the difference between two coprimes can be any number.
 All the pairs of twin prime numbers are also coprime, while all coprime numbers may or may not be twin primes.
 1 forms a coprime pair with every number, while it forms twin prime pair with only 3.
Coprime Numbers 1 to 100
In the list of coprime numbers from 1 to 100, there are many pairs that can be listed as coprime numbers based on the above properties. Some of the coprime number pairs that exist from 1 to 100 are (1, 2), (3, 67), (2, 7), (99, 100), (34, 79), (54, 67), (10, 11), etc. Try out forming more such pairs of coprime numbers by yourself. Here is Cuemath’s online coprime calculator for our ease.
Important Notes
 Two numbers are coprime if their GCF is 1. It can also be said that if the GCF of any two numbers is 1, those are coprime numbers.
 Coprime numbers need not necessarily be prime numbers. For example, 12 and 35 are coprime numbers, although, 12 and 35 are NOT prime numbers.
Tips and Tricks:
 Any two prime numbers are always coprime.
 Any two consecutive numbers are always coprime.
 1 forms a coprime pair with any other number.
 A prime number is coprime with any other number that is not its multiple.
 Two even numbers are NEVER coprime.
☛ Related Topics
 HCF of 2 Coprime Numbers
 Prime Numbers up to 100
 Whole numbers
 Natural Numbers
 Rational Numbers
 Real Numbers
 Is 2 a Prime Number?
 Is 41 a Prime Number?
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Coprime Numbers Examples

Example 1: Show that 161 and 192 are coprime numbers.
Solution:
We will find the HCF of the given numbers 161 and 192 using the division method.
The HCF of 161 and 192 is 1. Thus, they are coprime numbers.

Example 2: If 59 and 97 are coprime, what would be their HCF?
Solution:
It is given that 59 and 97 are coprime. They cannot have any common factor other than 1. Hence, their HCF is 1.

Example 3: State true or false with respect to coprime numbers.
a.) Coprime numbers need not necessarily be prime numbers.
b.) Two even numbers are always coprime.
Solution:
a.) True, coprime numbers need not necessarily be prime numbers.
b.) False, two even numbers are never coprime.
Practice Questions on Coprime Numbers
FAQs on Coprime Numbers
What are Coprime Numbers in Math?
Coprime numbers are those numbers that do not have any common factor other than 1. Coprime numbers form a pair of numbers that may not necessarily be prime numbers. For example, (6,35) is a set of coprime numbers, although 6 and 35 are composite numbers.
What is the Difference Between Prime and Coprime Numbers?
A prime number is a number that has exactly two factors, 1 and the number itself. For example, 2, 3, 7, 11 and so on are prime numbers. Coprime numbers are pairs of numbers whose HCF (Highest Common Factor) is 1. For example, (4,9) are coprimes because their only common factor is 1.
How to Find the Coprime of a Number?
The HCF of two coprime numbers is 1. Thus, to find the coprime number of a number, it is sufficient to find a number that is NOT divisible by any of the factors of the given number. For example, if we have a number 12 and we need to find a coprime number for 12, we can list 5 as its coprime number because 5 is not divisible by any of the factors of 12 (except 1). Therefore, (5,12) forms a pair of coprime numbers.
Which Numbers are Identified as Coprime Numbers?
A single number cannot be coprime. Only a pair of two numbers whose common factor is 1 forms a pair of coprime. In other words, two numbers are said to be coprime if their Highest Common Factor (HCF) is 1.
Are 18 and 35 Coprime Numbers?
Yes, 18 and 35 are coprime numbers. The factors of 18 are 1, 2, 3, 6, 9, 18. The factors of 35 are 1, 5, 7, 35. Here, 18 and 35 have no common factor other than 1. Thus, 18 and 35 are coprime.
Are Coprime Numbers Always Prime Numbers?
No, coprime numbers need not necessarily be prime numbers. For example, 18 and 25 are coprime numbers as their HCF is 1, although 18 and 25 are NOT prime numbers.
What is the HCF of Two Coprime Numbers?
The HCF of two coprime numbers is always 1. As 1 is the only common factor of two coprime numbers.
Are Two Successive Integers Always Coprime?
Yes, two successive positive integers are always coprime because one is an even number, the other is odd, and the HCF of two consecutive numbers is always 1.
How to Check if Two Numbers are Coprime?
In order to check if any two numbers are coprime or not, we need to find their Highest Common Factor (HCF). If their HCF is 1, then they are coprime numbers.
What are the Coprime Numbers from 1 to 100?
There are many pairs of co prime numbers from 1 to 100. A few of them can be listed as follows: (1, 2), (3, 67), (2, 7), (99, 100), (34, 79), (54, 67), (10, 11), and so on.
What is the LCM of Two Coprime Numbers?
The LCM of two co prime numbers is their product. This is because co prime numbers do not have any common factor other than 1. For example, if we take the coprime numbers 2 and 7 and find their LCM, we will get the LCM as 14 which also their product. (2 × 7 =14)
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