Co Prime Numbers are a pair of numbers with just one factor in common, which is 1. To put it another way, a pair of relatively prime numbers is said to be co-prime if their highest common factor (HCF) is 1.
Let’s learn the list, properties, and examples of co-prime numbers in detail.
Introduction to Co-Prime Numbers
Table of Content
What are Co Prime Numbers
Co-prime numbers are a pair of numbers that have no common factor other than 1.
Relatively prime or mutually prime numbers are other names for co-prime numbers.
Let us suppose there are two positive integers x and y that are coprime numbers if and only if they share only the number 1 as a common factor, with the result that HCF(x, y) = 1. The HCF of co-prime numbers is 1, making 1 their only common factor.
Co Prime Numbers from 1 to 100
There are many pairs of co-primes from 1 to 100.
Some examples from 1 to 100 are:
(3, 4)
(13,14)
(1, 97)
(23, 27)
(29, 31)
(45, 97) and so on.
We can write each number along with 1 as a co-prime pair.
List of Co Prime Numbers
Co prime pairs with numbers, starting from 1 are listed in the table below :
| Co prime with | Co-prime numbers pairs |
|---|---|
|
List of Co Prime Pairs |
|
| 1 | (1, 2), (1, 3), (1, 4), (1, 5) (1, 6),….., (1, 20),…. |
| 2 | (2, 3), (2, 5), (2, 7), (2, 9), …, (2, 15),….. |
| 3 | (3, 4), (3, 5), (3, 7), (3, 10), (3, 11),…., (3, 20),… |
| 4 | (4, 5), (4, 7), (4, 9), (4, 11), (4, 13), (4, 15),…. |
| 5 | (5, 6), (5, 7), (5, 8), (5, 9), (5, 11), (5, 12),… |
How To Find Co Prime Numbers
A pair of integers is co-prime if there is no other positive integer (other than 1) that can divide them both.
For instance, 21 and 22
21 and 22:
1, 3, 7, and 21 are the factors of 21.
1, 2, 11, and 22 are the factors of 22.Here, 21 and 22 only share a single factor, which is 1. Since they are co-prime, their HCF equals 1.
For instance, 15 and 20
15 and 20:
1, 3, 5, and 15 are the factors of 21.
1, 4, 5, and 20 are the factors of 27.Here, the numbers 1 and 5 are two factors that 21 and 27 both share. They are not co-prime and HCF is 5.
Properties of Co Prime Number
Co-prime numbers’ key properties are as follows :
- A pair of coprime numbers’ Highest Common Factor (HCF) is always 1.
- The result of two co-primes is always their Least Common Multiple (LCM).
- Every number and 1 makes a pair of co-prime numbers.
- Due to the fact that two even numbers always have 2 in common, they cannot both be co-prime numbers.
- Co-prime numbers always have co-prime products when added together.
- Two prime numbers are always co-prime. They only share 1 as their common factor.
- Co-prime numbers are all sets of two consecutive numbers.
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Difference between Prime and Co Prime Numbers
While prime numbers can be part of a co-prime pair, co-prime numbers themselves do not need to be prime.
Let’s compare prime numbers and co-prime numbers:
|
Prime vs. Co Prime Numbers |
||
|---|---|---|
| Aspect | Prime Numbers | Co-Prime Numbers |
| Definition | A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. | Co-prime numbers are two or more numbers that have no common positive divisor other than 1. |
| Divisibility | A prime number can be divided evenly only by 1 and itself. | Co-prime numbers can be divided evenly only by 1 when considered together. |
| Examples | 2, 3, 5, 7, 11, 13, 17, etc. | (15, 28), (9, 16), (8, 21), etc. |
| Number of Numbers | Concerns a single number. | Involves a pair or set of numbers. |
| Nature of Numbers | Always integers greater than 1. | Can be any integers, including 1 and negative numbers. |
| Common Factor | The only common factor is the number itself and 1. | The only common factor is 1. |
| Special Properties | All prime numbers are odd, except for 2, which is the only even prime number. | Co-prime numbers do not need to be prime; for example, 8 (which is not prime) and 9 are co-prime. |
Difference between Co Prime and Twin Prime Numbers
Co-prime numbers have their HCF as 1. Twin prime numbers, on the other hand, are prime numbers whose difference is always 2. For instance, 3 and 5 are twin prime numbers.
Let’s make a comparison between co-prime and twin prime numbers are :
| Feature | Co Prime Numbers | Twin Prime Numbers |
|---|---|---|
|
Co Primes vs. Twin Prime Numbers |
||
| Nature of Numbers | Can be composite or prime | Always prime |
| Difference Between Numbers | Can be any number | Always 2 |
| Relationship to Each Other | May or may not be twin primes | Always co-prime |
| Special Pairs | Every number forms a co-prime pair with 1 | Only the pair (3, 1) is considered as twin primes. |
Solved Examples on Co Prime Numbers
Here we have solved some examples on co-prime numbers for your help.
1: Check if 259 and 256 are co-prime numbers.
Solution:
Given numbers are 259 and 256.
1,2,4,8,16,32,64,128 and 256 are the factors of 256.
1,7,37 and 259 are the factors of 259.
They only have 1 as their common factor hence they are co-prime numbers.
2: Check whether 28 and 21 are co-prime numbers.
Solution:
Given numbers are 28 and 21.
1,3,7 and 21 are the factors of 21.
1,2,4,7 and 28 are the factors of 28.
21 and 28 have 1,7 as their common factors. Since their highest common factor is 7.Hence, they are not co-prime numbers.
Co Prime Numbers Practice Exercise
Here are some practice questions on co prime numbers for you to solve :
1. If the product of two co prime numbers is 117, then find their LCM.
2. Are 17 and 68 co prime numbers? Justify.
3. Are 30 and 415 co prime numbers? State your reasons.
4. Are 216 and 215 co prime numbers?
5. Are 18 and 35 Coprime Pairs?
List of Co Prime Numbers- FAQs
1. What are Co Prime Numbers?
Coprime numbers are ones with just one common factor in common, which is 1. To put it another way, a pair of numbers is said to be co-prime if their highest common factor(HCF) is 1.
2. How many co prime numbers are there from 1 to 100?
Co-prime numbers always come in a pair rather than individual numbers. Therefore, the question of how many co-prime numbers are there from 1 to 100 doesn’t have a straightforward answer. It depends on the pairs of numbers we have considered.
3. How to Find the Co-prime of a Number?
To find the co-prime of a number, you need to identify another number whose HCF with the given number is 1. You can achieve this by selecting numbers that don’t have common prime factors. The resulting pair of numbers will be co-prime.
4. What is the difference between prime and co prime numbers ?
Prime numbers are those who have only 1 and they themselves as their factors while co-prime numbers exist in pair if the HCF of two numbers is 1.
5. What is the difference between co prime and twin prime numbers?
Co-prime numbers have their HCF as 1. Twin prime numbers, on the other hand, are prime numbers whose difference is always 2.
6. What is the LCM of two co prime numbers?
The LCM of two co-prime numbers is equal to the product of those two numbers. This is because co-prime numbers have no common positive divisors other than 1.
7. What is the HCF of two co prime numbers?
The HCF of two co-prime numbers is always 1. This is because co-prime numbers are defined as a set of numbers that have no other common positive divisor except for 1.