What are the Co-Prime Numbers?
Co-Prime Numbers are a set of Numbers where the Common factor among them is 1. It implies that the HCF or the Highest Common Factor should be 1 for those Numbers. Co-Prime Numbers are also referred to as ‘Relatively Prime Numbers’.
Eg: If x and y are the Co-Prime Numbers set, then the only Common factor between these two Numbers is 1.
Co-Prime Numbers from 1 to 100
Co-Prime Numbers are none other than just two Numbers that have 1 as the Common factor. Some of these Co-Prime Numbers from 1 to 100 are -
There are several pairs of Co-Primes from 1 to 100 which follow the above properties. Some of them are:
(1, 99)
(14, 15)
(28, 57)
(29, 31)
(23, 1)
(59, 97) etc.
Co-Prime Numbers are sets of Numbers that do not have any Common factor between them other than one. This means that their highest Common factor (HCF) is 1.
There should be at least two Numbers in order to form Co-Primes.
Co-Prime Numbers are also called relatively Prime Numbers.
How to Check if the Given Set of Numbers is CoPrime
By the definition of CoPrime Numbers, if the given set of Numbers have 1 as an only Common factor then the given set of Numbers will be CoPrime Numbers. Let us Consider a set of two Numbers:
1. 14 and 15
Factors of 14 are 1, 2, 7 and 14.
Factors of 15 are 1, 3, 5 and 15.
The Common factor of 14 and 15 is only 1. So, 14 and 15 are CoPrime Numbers.
2. 11 and 17
Factors of 11 are 1 and 11.
Factors of 17 are 1 and 17.
Common factors of 11 and 17 are only 1. So, 11 and 17 are CoPrime Numbers.
3. 15 and 18
Factors of 15 are 1, 3, 5 and 15.
Factors of 18 are 1, 2, 3, 6, 9 and 18.
Common factors of 15 and 18 are 1 and 3. Since the given set of Numbers have more than one factor as 3 other than factor as 1. So, 15 and 18 are not CoPrime Numbers.
Properties of Co-Prime Numbers
Some of the properties of Co-Prime Numbers are as follows.
1 is CoPrime with every Number.
Every Prime Number is Co-Prime to Each Other:
As every Prime Number has only two factors 1 and the Number itself, the only Common factor of two Prime Numbers will be 1. For example, 11 and 17 are two Prime Numbers. Factors of 11 are 1, 11 and factors of 17 are 1, 17. The only Common factor is 1 and hence is Co-Prime.
Any two successive Numbers are always CoPrime:
Consider any Consecutive Number such as 2, 3 or 3, 4 or 14 or 15 and so on; they have 1 as their HCF.
The sum of any two Co-Prime Numbers is always CoPrime with their product.
2 and 3 are Co-Prime and have 5 as their sum (2+3) and 6 as the product (2×3). Hence, 5 and 6 are Co-Prime to each other.
Solved Examples
1. Check CoPrime Numbers from the Given Set of Numbers
21 and 24
13 and 15
17 and 18
Ans.
a) 21 and 24 are not a CoPrime Number because their Common factors are 1and 3
b) 13 and 15 are CoPrime Numbers because they are Prime Numbers.
c) 17 and 15 are CoPrime Numbers because they are two successive Numbers.
2. What is the Difference Between Prime Numbers and CoPrime Numbers?
Ans. A Prime Number is defined as a Number which has no factor other than 1 and itself.
But, CoPrime Numbers are Considered in pairs and two Numbers are CoPrime if they have a Common factor as 1 only. Their HCF is 1.
FAQs on Co-Prime Numbers
1. How Can I Find the Co-prime of a Number?
The Highest Common Factor/ HCF of two numbers has to be 1. In order to find a co-prime number, you have to find another number which can not be divided by the factors of another given number.
2. Can a Number be Considered as a Co-prime Number?
No, a single number cannot be considered as a co-prime number as the HCF of two numbers has to be 1 in order to recognise them as a co-prime number.
3. Do 27 and 34 form a Co-prime Pair?
Yes, these are a co-prime pair.
4. If 19 and 23 Co-prime Numbers, then What Would be their HCF?
As it is already given that 19 and 23 are co-prime numbers, then their HCF can be nothing other than 1.
5. Are 2 and 97 Co-prime Numbers?
Yes. 2 and 97 form a co-prime pair.
6. What are the properties of Co-Prime Numbers?
Some qualities that are mentioned below can help you identify Co-Prime Numbers quickly:
When two CoPrime Numbers are added together, the HCF is always 1. For instance, because 5 and 9 are CoPrime Numbers, HCF (5, 9) = 1.
The product of two Co-Prime Numbers is always the LCM of their LCM. 5 and 9 are Co-Prime Numbers, for example. As a result, LCM (5, 9) = 45. 1 is a Co-Prime Number pair with all other Numbers.
As they always have 2 as a Common element, two even integers cannot be Co-Prime Numbers.
The product of two Co-Prime Numbers will always be Co-Prime. 5 and 9 are Co-Prime Numbers, for example. 5 + 9 = 14 is Co-Prime with 5 multiplied by 9 = 45 in this case.
Every Number and 1 form a Co-Prime Number pair.
As they always have 2 as a Common element, two even integers cannot be Co-Prime Numbers.
Co-Prime Numbers are always two Prime Numbers. They only have one thing in Common. Consider the Numbers 29 and 31. Only 1 and 29 are Prime factors in the Number 29. Only 1 and 31 are Prime factors in the Number 31. Prime Numbers are 29 and 31. They only have one thing in Common: 1. As a result, they are Co-Prime. Any two Prime Numbers can be checked to see if they are Co-Prime. 2 and 3, for example, 5 and 7, 11 and 13, and so on.
Co-Prime Numbers are all pairs of two Consecutive Numbers. The Common factor of any two Consecutive Numbers is 1. To learn more, you can click here.
7. What are Co-Prime and twin Numbers?
Co-Prime Numbers are those with an HCF of 1 or two Numbers with only one Common Component. Twin Prime Numbers, on the other hand, are Prime Numbers whose difference is always 2. Three and five, for example, are twin Prime Numbers.
Co-Prime Numbers can also be Composite Numbers, while twin Numbers are always Prime Numbers.
The difference between two twin Primes is always 2, although the difference between two Co-Primes might vary.
All twin Prime Number pairs are also Co-Prime Numbers, albeit not all Co-Prime Numbers are twin Primes.
Every Number forms a Co-Prime pair with 1, but only 3 makes a twin Prime pair.
8. What are important points to remember about Co-Prime Numbers?
The important tricks and tips to remember about Co-Prime Numbers.
Tricks and Tips:
If the GCF of two Numbers is 1, they are Co-Prime, and vice versa.
It is not necessary for Co-Prime Numbers to be Prime Numbers. 12 and 35, for example, are Co-Prime Numbers. 12 and 35, on the other hand, are not Prime Numbers.
Co-Prime Numbers are any two Prime Numbers.
Any two Numbers in a row are Co-Prime.
Any other integer and 1 create a Co-Prime pair.
Any Number that is not its multiple is Co-Prime with a Prime Number.
Co-Prime Numbers are never two even Numbers.
9. What are the Co-Prime Numbers from 1-100?
The Co-Prime Numbers from 1-100 are:
There are many pairs that can be listed as Co-Prime Numbers in the list of Co-Prime Numbers from 1 to 100 based on the preceding properties. (1, 2), (3, 67), (2, 7), (99, 100), (34, 79), (54, 67), (10, 11), and so on are some of the Co-Prime Number pairings that exist from 1 to 100. Experiment with generating more pairs of Co-Prime integers on your own.
To find Co-Prime Numbers, follow these steps:
To determine if two integers are Co-Prime, we must first determine their GCF. We can say they are Co-Prime if their GCF is 1.
Consider the Numbers 5 and 9 as an example. 1 and 5 are the factors of 5. The nine factors are 1, 3, and 9. The factor that both 5 and 9 have in Common is 1. GCF = 1 for (5, 9) As a result, the Numbers (5, 9) are a Co-Prime pair.
10. How did Euclid prove that there are infinite Prime Numbers?
Euclid utilised another foundational theorem, the premise that "any natural Number may be expressed as a product of Prime Numbers," to prove that there are infinitely many Prime Numbers. It is simple to believe that the last claim is true. If you choose a Number that is not Composite, it is Prime in and of itself. Otherwise, you might express your chosen Number as the product of two smaller Numbers. You have stated your Number as a product of Prime Numbers if each of the smaller Numbers is Prime. If this is not possible, write the smaller Composite Numbers as products of smaller Numbers, and so on. You keep substituting any of the Composite Numbers with products of smaller Numbers in this manner.
As this cannot be done indefinitely, the process must Come to an end, and all of the smaller Numbers you end up with can no longer be broken down, indicating that they are Prime Numbers. Kindly visit the Vedantu website and app for free study materials.
