Question

Explain why the greatest common factor of two numbers is sometimes 1.

Answer 1

Step-by-step explanation:

The greatest common factor of two numbers is sometimes 1 when they are coprime to each other.

Coprime numbers are those numbers who are relatively prime.

Now, prime numbers are those numbers who are divisible by 1 and itself only.

So, eventually when we going to find the greatest common factor of two prime numbers it comes out to be 1 only.

For example, we takes two numbers 2 and 5 ,

Factor of 2 = 1,2

Factor of 5= 1,5

So , 1 is only common factor between them.

Answer 2

Because one of the numbers can be prime numbers, for example the greatest common factor of 12 and 13 it's 1 because 13 it's a prime number or because they don't have common prime factors.Prime numbers are the numbers who can be divided just by 1 and themselves.