FINDING RELATIVELY PRIME NUMBERS WITH EXAMPLES

RELATIVELY PRIME NUMBERS

Relatively prime numbers are those which have only one common factor which is the number 1. Now, before we go any further, it is important to understand the meaning of prime numbers. Prime numbers are those which have two factors only, namely the number itself and 1. These numbers are not divisible by any other number. For example, 2, 3, 5, 7, 11, 13, 19 and so on are all prime numbers. The numbers that are not prime are called composite numbers. 1 is neither a prime nor a composite number. 

Relatively prime numbers can also be called co-primes or mutually prime numbers. It is a set of numbers that has only 1 as the common divisor. Relatively prime numbers don’t need to be prime numbers only. They can be composite numbers as well or one can be prime and the other can be a composite number. 

For example, consider the following set of numbers:

1. 4, 19 – These numbers have only one factor in common which is 1 so they are co-primes. Here, one number is composite and the other is prime.
2. 2, 7 – They are both prime numbers and the only common divisor is 1. Thus, making them co-prime numbers.
3. 4, 9 – Though both these numbers are composite, the only factor common among them is 1.

HOW TO IDENTIFY RELATIVELY PRIME NUMBERS

The best way to identify co-primes is to find the greatest common divisor or the highest common factor (HCF). HCF is simply the highest number that can divide both the numbers into consideration. For example, consider the numbers 18 and 21.

Factors of 18 are 1, 2, 3, 6, 9 and 18.

Factors of 21 are 1, 3, 7, 21.

The common factors are 1 and 3 but the highest of the two is 3 so the HCF of 18 and 21 is 3. 

In the case of relatively prime numbers, we can find the HCF and if it is 1 then they are co-primes. 

For example 6 and 17.

Factors of 6 are 1, 2, 3 and 6.

Factors of 17 are 1, 17.

The only and the highest factor that is common is 1. Therefore, 6 and 17 are mutually prime or relatively prime.