What are Co-Prime Numbers?
Co-prime numbers are numbers that have no common factor apart from the number 1. Let two numbers be ‘a’ and ‘b’ such that the common factor between ‘a’ and ‘b’ is only the number 1 or the GCF of (a, b) = 1, then ‘a’ and ‘b’ are called co prime numbers.
Rules for Spotting Two Co-Prime Numbers
- 1 is coprime with every number.
- Two consecutive natural numbers are always coprime.
Example: (2, 3), (5, 6), (12, 13)and so on. - Two consecutive odd numbers are always coprime.
Example: (3, 5), (7, 9), (11, 13)and so on. - Two even numbers can never be a co-prime number as all the even numbers have a common factor as 2.
Example: (2, 4) is not a co-prime number because
Factor of 2 = 1 and 2
Factor of 4 = 1, 2 and 4
The common factor of (2, 4) is 2. - Two prime numbers are always coprime numbers.
Example: (2, 3), (5, 7), (13, 17)and so on.
Fun Facts
- Two numbers are said to be coprime if their GCF is 1 and vice versa.
- Co-prime numbers don’t need to be prime numbers. For example, 14 and 43 are co-prime numbers, although 14 and 43 are ‘not’ prime numbers.
What are Composite Numbers?
Composite numbers are numbers that have more than two positive factors. In other words, the numbers that don’t belong to the group of prime numbers are composite numbers — except 0 and 1. The numbers 0 and 1 are special numbers that neither belong to prime numbers nor composite numbers. Some examples of composite numbers are 4, 6, 8, 9 and 12.
Solved Co-Prime Number Examples
Example 1: Check whether 5 and 14 are coprime numbers?
Solution:
Factors of 5 = 1 and 5.
Factors of 14 = 1, 2 and 7.
We can see 5 and 14 have only one common factor i.e 1.
Hence,5 and 14 are co-prime numbers.
Example 2: Check whether 9 and 12 are coprime numbers?
Solution:
Factors of 9 = 1 and 3.
Factors of 12 = 1, 2 and 3.
The common factors between 9 and 12 = 1 and 3.
We can see 9 and 12 have common factors other than 1.
Hence,9 and 12 are not co-primes.
Example 3: Write the coprime numbers between 1 and 50, and identify the count of these numbers?
Solution:
Co prime numbers between 1 and 50 are (2, 3), (3, 5), (5, 7), (11, 13), (17, 19), (21, 22), (29, 31) and (41, 43).
Hence, there are 8 coprime numbers between 1 and 50.
A prime number is a number that has no factor other than 1 and itself.
Example: 2, 3, 5, 7 and 11 are all prime numbers.
Conversely, co-primes are written as a group of two numbers and they are considered co-primes if they have no common factors other than 1.
Example: (2, 3), (3, 5),(4, 5)and (7, 11)and so on.
- To identify coprime pairs, we find the factors of all the given numbers first.
- By identifying the common factor, and if they don’t have a common factor other than 1, they will certainly be coprime.
A twin prime is a pair of prime numbers that are 2 less or 2 more than each other.
Example: 3 and 5, 5 and 7, 11 and 13, 17 and 19 and so on.
A twin prime is a pair of prime numbers that are 2 less or 2 more than each other. Additionally, coprime numbers can be any pair of numbers whose greatest common factor is 1. That means two composite numbers can be coprime numbers if their GCF is 1.
The factor of any number divides the number exactly without leaving any remainder.
For example, the number 7 divides the number 14 exactly 2 times without leaving any remainder. Hence, 7 is a factor of 14.