 # Co-Prime Numbers

### Introduction

Wondering what are co-prime numbers? Also known as mutually prime or relatively prime numbers, the pre-requisite of co-prime numbers is that there must be 2 numbers. In the theory of number system, the numbers are classified as per their properties. Consider the set of 2 numbers, in case they don’t have any positive integer which can divide both, other than 1, that pair of numbers is co-prime. There are various co-primes pairs from 1-100 following the specific properties. A few of them include (28, 57), and (13, 14) etc. Let’s go through this guide targeted the interesting co-prime numbers concept.

### Definition

Now, let’s come towards the main question i.e., what is the definition of co-prime numbers? “Co” means the “pair”. Hence, you can define the pair of integers, say a & b, as primes or co-prime to each other or relatively prime or mutually prime if:

• In other words, HCF of 2 numbers is 1.
• The only positive integer which divides both of them for giving the remainder 0 is 1.
• Co-prime numbers are signified as GCF (a, b)=1 or (a, b)=1 or as “a is prime to b”.

Now, let’s see how to look for co-prime numbers?

Are 15 and 6 co-prime numbers?

Take a look – Factors of 15= 1, 3,5,15

Factors of 6= 1,2,3,6

While comparing factors of these 2 numbers 15 and 6, you see that both of these numbers have factors 3 and 1 in common. For this pair, the HCF is 3. Hence, this pair is not co-prime.

### Properties

Below mentioned are a few properties of the co-prime numbers –

• 1 is co-prime with all numbers.
• Looking for Co-prime numbers from 1 to 100? Always remember that any 2 prime numbers are co-prime to each other. While all the prime numbers have only 2 factors i.e., 1 and the number itself and the single common factor of 2 prime numbers will be 1. For instance, 2 & 3 are the two prime numbers. Factors of 3 are 1, 3 and factors of 2 are 1, 2. The single factor is 1 and thereby, they are co-prime.
• Any 2 successive integers/numbers are always co-prime. Take up the consecutive numbers like 2, 3 or 3, 4 or 5, 6 & so on. All of these have 1 as the HCF.
• Sum of any 2 co-prime numbers is always co-prime with the product. For instance, 2 & 3 are co-prime as well as have 5 as the sum (2+3) & 6 as their product (2×3). Thereby, 5 and 6 are co-prime to each other.
• 2 even numbers can never form the co-prime pair since every even number has the common factor as 2.
• In case two numbers have the unit digits like 0 and 5, they aren’t co-prime to each other. For instance, 10 & 15 aren’t co-prime as the HCF is 5 (or divisible by 5).

Examples

Check out these examples of co-prime numbers to understand this concept better –

Ex. 1 – Take 2 numbers i.e., 66 & 1010

Factors of 66 – 1, 2, 3, and 66

Factors of 1010 – 1, 2, 5, and 1010

The factors common to both 66 & 1010 are 11 & 22.

So, GCF (6, 10) = 2.

Thereby, (6, 10) is not the co-prime pair.

Ex. 2 – Take 2 numbers i.e., 55 & 99

Factors of 55 – 1, 11 & 88

Factors of 99 – 1, 3, & 99

The factor common to both 55 & 99 is 1.

So, GCF (5, 9) = 1.

Thereby, (5, 9) is the co-prime pair.

Ex. 3 – Take 2 numbers i.e., 150 & 295

Factors of 150 – 2, 3, 5

Factors of 295 – 5, 59

The factor common to both 150 & 295 is 5.

So, GCF (150, 295) = 5.

Thereby, (150, 295) is not the co-prime pair.

Ex. 4 – Take 2 numbers i.e., 13 & 31

Factors of 13 – 1, 13

Factors of 31 – 1, 31

The factor common to both 13 & 31 is 1.

So, GCF (13, 31) = 1.

Thereby, (13, 31) is the co-prime pair.

### FAQs

Q – How is the definition of co-prime numbers different from the ones of prime numbers?

A – The prime number is described as the one which has no other factor than 1 and itself. On the contrary, the co-primes are regarded in pairs & 2 numbers are considered as the co-primes in case they don’t have any other common factor than 1.

Q – Is 1 co-prime to every number?

A – Yes, when it comes to Co-prime numbers from 1 to 100, 1 is co-prime to every number. As HCF of 1 & any other number is 1 itself. Thereby, going by the definition of the co-prime number, 1 is considered as co-prime with every number.

Q – How do you look for a number’s co-prime?

A – For finding a number’s co-prime, firstly look for the number’s factors. Afterwards, pick a number & find the chosen number’s factors. Every number that does not have the common factor other than 1 will be co-prime of the specified number.

Q – What is the co-prime numbers’ LCM?

A – LCM of the given co-prime pair is equivalent to the 2 numbers’ product. For instance, 10 & 21 are co-prime. LCM of 21 and 10 will turn out to be 210 i.e., (21×10).

Q – In case 2 numbers are co-prime, then is one of them always divisible by the other one?

A – No, it isn’t. In case the number is divisible by the pair’s other number, then that pair is not the co-prime one.

#### Conclusion

The journey of math around the co-prime numbers begins with what the student knows already, & goes on to innovatively generating the fresh concept in young minds. Moreover, knowing about the Co-prime number list is important as it helps you in understanding a lot of mathematics concepts with sheer ease. Also, you can take the help of Edulyte.com i.e., the reliable student-oriented online learning platform. Edulyte has plenty of subject professionals who are experienced and know how to make the students understand even the toughest of concepts with sheer ease. Its experts stay engaged with students at all the stages of the study procedure & offer them sufficient resources and lessons which build the enthusiasm for learning and growing. As a result, they prepare for their maths exam effectively with online Maths classes and pass with flying marks.

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