Precise NumbersDate: 10/18/2001 at 21:28:55 From: Ryan Adams Subject: Precise Numbers I have a contest problem about precise numbers which the problem alleges is in the same category as proper divisors. I can't find any formulas to figure them out. The problem says that a precise number occurs when its proper divisors multiplied together equal the number. For example, 6 is a precise number because 1*2*3 = 6. I'm wondering if there is another name or formula that would help me figure out the problem. Thanks, Ryan Date: 10/19/2001 at 17:32:26 From: Doctor Ian Subject: Re: Precise Numbers Hi Ryan, I'm not sure what kind of 'formula' you're looking for, but maybe this will be helpful. First, just to make sure that you know what it means to break a number into prime factors, take a look at Finding All the Factors of a Number http://mathforum.org/dr.math/problems/shaya.09.10.01.html If a number has exactly two prime factors, p and q, then the only proper factors of the number will be 1, p, and q; and when you multiply these together, 1 * p * q you get the number itself. Note that if you have more than two prime factors (p, q, and r), then you get extra proper factors: 1, p, q, r, pq, pr, qr. When you multiply these together you get something larger than the original number: 1 * p * q * r * pq * pr * qr \___________/ this is the number itself On the other hand, if the number is prime, then the only proper divisor is 1. So in order for a number to be what you're callling a 'precise number', it has to have exactly two prime factors. So now we can start cranking out 'precise numbers': * 2 3 5 7 11 2 4 6 10 14 22 3 9 15 21 33 5 25 35 55 7 49 77 11 121 and so on. So I guess this is a kind of 'formula' after all. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 10/20/2001 at 13:02:42 From: Ryan Adams Subject: Re: Precise Numbers Yes - thank you very much. Ryan |
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