Relative PrimesDate: 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/ |
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