Relative Primes

Date: 11/24/97 at 22:13:24
From: Athena
Subject: Relative Primes

What IS relatively prime? I have some homework with no basic 
instructions other than using these numbers: 8, 9, 11, 12, 14, 15, 21, 
24, 25, 28 to answer the questions below. The first one goes: Which 
numbers are relatively prime to 4? Then Which numbers are relatively 
prime to 6? and so on.....

I also have other questions of my own... can two even numbers be 
relatively prime? How about odd?

We have been working on factors and have never touched on "relatively 
prime." What is the connection between factors and relatively prime? 

Thank you,
Athena

Date: 11/25/97 at 16:58:39
From: Doctor Terrel
Subject: Re: Relative Primes

Dear Athena,

In simple terms, two (or more) numbers are said to be relatively prime 
if their "GCF" (greatest common factor) is 1.

My favorite teaching example is to use 14 and 15, about which I am 
quick to point out that "Neither of them is prime, but taken as a 
pair, they are relatively prime numbers. Proof? The factors of 14 are 
1, 2, 7, and 14.  The factors of 15 are 1, 3, 5, and 15. The greatest 
common factor (in fact the only one) they share is one (1)."  End of 
story.

Actually you've been using the idea of relatively prime numbers every 
time you reduce a fraction to its lowest terms. For example, 15/22 is 
in lowest terms because there is no number that is a common factor 
(other than 1) by which we can divide the numbers 15 and 22.

Now your homework should make some sense. Okay?

-Doctor Terrel,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/