# Thread: Are 5 and 20 relatively prime with each other?

1. Hi all, quick question regarding relatively prime numbers.

Factors of 5: 1, 5
Factors of 20: 1, 2, 4, 5, 10, 20
Greatest common factor = 5

Since the greatest common factor of both numbers is 5, does that mean these numbers are not relatively prime towards each other? Or does 5 not count as a factor since it is one of the numbers I am checking?

Thanks!

2.

3. Two numbers are relatively prime if they have no factors in common other than 1. So those two numbers are not relatively prime - because of the common 5, which does count as a factor.

4. Originally Posted by southp4w
Hi all, quick question regarding relatively prime numbers.

Factors of 5: 1, 5
Factors of 20: 1, 2, 4, 5, 10, 20
Greatest common factor = 5

Since the greatest common factor of both numbers is 5, does that mean these numbers are not relatively prime towards each other? Or does 5 not count as a factor since it is one of the numbers I am checking?

Thanks!
By definition, no, they are not relatively prime.

The test is easy:

If the largest common prime factor exceeds 1, they are not relatively prime. That's it.

Here, 5 exceeds 1, even for extremely large values of 1.

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