Co Prime Numbers: Definition, Properties and Examples

Co Prime Numbers: When a set of integers or numbers has only number 1 as the common factor then they are known as Co Prime Numbers. Co Prime Numbers are otherwise called relatively prime or mutually prime numbers. In order to form a Co Prime number, we need to have at least two numbers. Furthermore, every prime number is co-prime to each other.

It is also important to note that the sum of any two co-prime numbers is coprime with their product. In this article, we have provided all the important information like co prime number meaning, list, properties, solved examples, etc. Scroll down to learn more about co prime numbers.

What Are Co Prime Numbers?

Co Prime Number Definition in Maths: The definition of Co-Prime Numbers is, “When two numbers do not have any common factor other than 1, then they are called Co-Prime Numbers”. It indicates that the Highest Common Factor or HCF of two Co-prime numbers should be 1 for those numbers. Co-prime numbers are also called “Relatively Prime Numbers”.

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Here the factors of 3 are 1, 3 and factors of 10 are 1, 2, 5, 10. The only common factor of 10 and 3 is 1. So {3,10} are co-prime numbers.

Properties of Co-Prime Numbers

The properties of Co Prime Numbers are given below:

1. Number 1 is co-prime with every number.
2. Two prime Numbers together always form co-prime numbers. Prime numbers always have two factors – 1 and the number itself. So, the common factor between two prime numbers will always be 1.
   Example: 2, 3 (Factors of 2 are 1, 2 and Factors of 3 are 1, 3. So 2,3 are Prime Factors.)
3. Any two consecutive integers or numbers will always be Co-Prime numbers since the successive numbers’ HCF will be always 1.
   Example: {1,2}, {2,3}, {3,4}, {4,5}, {5,6} and so on.
4. Two even numbers cannot form a co prime number since the even numbers will always have 2 as their common factor.
5. If two numbers or integers have their unit number as 0 and 5, they cannot be co prime numbers.
   Example: {30, 35} cannot be co prime numbers since both the numbers are divisible by 5.

Co Prime Number From 1 to 50

The list of co prime numbers from 1 to 50 are given below:

Solved Examples on Co Prime Numbers

Go through the following solved examples:

Q.1: Are 18 and 35 Coprime Numbers?
Ans: To check if 18 and 35 are co prime numbers, we will have to check the common factors of 18 and 35.
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
So, the common factors of 18 and 35 are “1”.
Thus {18,35} are co prime numbers.

Q.2: Are 4 and 8 Coprime numbers?
Ans: To check if 4 and 8 are co prime numbers, we have to check the common factors or 4 and 8.
Factors of 4 = 1, 2, 4
Factors of 8 = 1, 2, 4, 8
Since there is more than 1 common factor between 4 and 8, {4,8} are not co prime numbers.

Q.3: Are 30 and 45 Coprime Numbers?
Ans: According to the Co Prime properties, two numbers whose unit number is 0 and 5 are not co prime numbers as the numbers will be divisible by 5.
Explaination:
Factors of 30 = 1, 2, 3, 5, 10, 15
Factors of 45 = 1, 3, 5, 7, 15, 45
Since there are more than 2 common factors, {30,45} aren’t co prime numbers.

Co Prime Number in Hindi

The Co-Prime number meaning in Hindi is given below for easy understanding of students belonging to Hindi medium or those from Hindi-belt.
“वह संख्या जो अपने अलावा किसी भी अन्य दो पूर्ण संख्या (whole Number ) के गुणा करने से बन सके, उसे Composite number या भाज्य संख्या कहा जाता है। उधारण के लिए 18 एक Coprime number है।

FAQ

The frequently asked questions on Co Prime Numbers are given below:

Q.1. Explain co prime numbers with examples.
Ans. Any two numbers which have “1” as the only common factor are known as co prime numbers. Example of co prime numbers are {1,2}, {2,3}, {10, 11} etc.

Q.2. Is 25 a Coprime number?
Ans. We need at least 2 numbers to check if they are co prime numbers. The possible co prime numbers with 25 are {1,25}, {2,25}, {3,25}, {4,25}, etc.

Q.3. Are 9/10 coprime numbers?
Ans. Yes, {9,10} are coprime numbers.

Q.4. Is 216 and 215 a co prime number?
Ans. Any two consecutive numbers are co prime numbers. So, 215 and 216 are co prime numbers.

Q.5. Are prime and co prime numbers the same?
Ans. No, a Prime Number is a number that has 1 and the number itself as the factors. Whereas, Co Prime Numbers are the numbers that have only 1 as their common factors.

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