Relatively Prime Numbers

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Relatively prime numbers are two integer which have only 1 as their common factor. Relatively prime numbers are also called as co-prime numbers or mutually prime numbers. This concept is very useful concept in mathematics. If a and b are any two integers they are called relatively prime numbers if both are divisible by number 1 and have no other common divisor. This can also be explained as the greatest common divisor for a, b is 1. Hence GCD of (a, b) is one. 
 
Example 1: Find if 30 and 77 are relatively prime numbers.

Solution: Given are numbers 30 and 77.

The number 30 can be written as: 30 = 1 * 2 * 3 * 5.

The number 77 can be written as: 77 = 1* 7 * 11.

Hence from the above representation of the numbers 30 and 77 it’s determined that they have a common factor 1.

Hence 30 and 77 are relatively prime numbers.
 
Example 2: Find if 48 and 36 are relatively prime numbers.

Solution: Given are numbers 48 and 36.

The number 48 can be written as: 48 = 1 * 2 * 2 * 2 * 2 *3 = 1 * 24 * 3.

The number 36 can be written as: 36 = 1* 2 * 2* 3 * 3 = 1 * 22 *32.

Hence from the above representation of the numbers 48 and 36 it’s determined that they have a common factors 1, 22 and 3.

Hence 48 and 36 are not relatively prime numbers.
          

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