Co Prime Numbers are the set of numbers in which only number one is the common factor. The Highest Common factor for the set of numbers should be one in this case. We will be reading all the properties related to the co-prime number.
Co prime numbers are those numbers that have only one common factor, namely 1. That means a pair of numbers are said to be co-prime when they have their highest common factor as 1. There are different ways to define co-prime numbers. In this article, you will understand what are coprime numbers in Math, and how to identify the co-prime number using simple tricks and tips along with examples. Edureify will provide a detailed article on coprime numbers which will help the students in many exams.
How to Find Co-prime Numbers?
Consider a set of two numbers, if they have no positive integer that can divide both, other than 1, the pair of numbers is co-prime. We will see through examples to have a clear vision about the same.
Example 1: 22 and 23
For 22 and 23:
- The factors 22 are 1, 3, 7, and 21.
- The factors 23 are 1, 2, 11, and 22.
Here 22 and 23 have only one common factor which is 1. Hence, their HCF is 1 and is co-prime.
Example 2: 21 and 27
For 21 and 27:
- The factors of 21 are 1, 3, 7, and 21.
- The factors of 27 are 1, 3, 9, and 27.
Here 21 and 27 have two common factors; they are 1 and 3. HCF is 3 and they are not co-prime.
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Properties of Co-Prime Numbers
Some of the properties of co-prime numbers are as follows. These are called tricks to identify the pairs of co-prime numbers quickly.
- One is co-prime:- 1 is co-prime with every number.
- Co-prime + co-prime = Co-prime:– Any two prime numbers are 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, 2 and 3 are two prime numbers. Factors of 2 are 1, 2, and factors of 3 are 1, 3. The only common factor is 1 and hence they are co-prime.
- Two successive integers are always co-prime:- Any two successive numbers/ integers are always co-prime.
Take any consecutive numbers such as 2, 3, or 3, 4 or 5, 6, and so on; they have 1 as their HCF.
- The Sum of two co-prime is always co-prime:- The sum of any two co-prime numbers is always co-prime 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.
- Two even numbers can’t be co-prime:- Two even numbers can never form a co-prime pair as all the even numbers have a common factor as 2.
- Numbers with unit digit 0 and 5 is not a co-prime number:– If two numbers have their unit digits like 0 and 5, then they are not co-prime to each other. For example, 10 and 15 are not co-prime since their HCF is 5 (or divisible by 5).
Frequently Asked Questions
Q: What are Co-prime Numbers?
Ans:- Co-prime numbers or relatively prime numbers are those numbers that have their HCF (Highest Common Factor) as 1. In other words, two numbers are coprime if they have no common factor other than 1.
Q:- What is the difference between prime and Co-prime numbers?
Ans:- A prime number is defined as a number that has no factor other than 1 and itself. On the contrary, co-primes are considered in pairs and two numbers are co-prime if they have no common factors other than 1.
Q:- How do you Find the Co-prime of a Number?
Ans:- To find the co-prime of a number, find the factors of the number first. Then, choose any number and find the factors of the chosen number. All the numbers which do not have any common factor other than 1 will be the co-prime of the given number.
Q:- Are 18 and 35 Co-prime Numbers?
Ans:-Yes, 18 and 35 are co-prime numbers. The factors of 18 are 1, 2, 3, 6, 9, and 18 while the factors of 35 are 1, 5, 7, and 35. Since the HCF is 1, they are co-prime.
Q:- Is 1 Co-prime to All numbers?
Ans:-Yes, 1 is co-prime to all the numbers. Since HCF of 1 and any number is 1 itself. Hence, by the definition of co-prime numbers, 1 is said to be co-prime with all numbers.
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