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Magic 8's (Posted on 2006-09-18) Difficulty: 4 of 5
There is a number which has 8 divisors including, 8, itself, and 1. There is also a number which has 18 divisors, including 18, itself and 1. The difference between these numbers is 28. What are the two numbers?

No Solution Yet Submitted by joshua    
Rating: 4.0000 (2 votes)

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re: Solution | Comment 6 of 8 |
(In reply to Solution by Dej Mar)

"For the second number to have exactly 18 different factors to include 1 and 18, the number must be composed of 1 and the primes 2, 2, 3, 3 and y where y in not 2 or 3."

2^2 * 3^5 and 3^2 * 2^5 also have 18 different factors, including 1 and 18.  The latter can be ruled out by being a multiple of 8 (a real candidate must be a multiple of 4 but not of 8, to complement 28), but the former had to be tried.


  Posted by Charlie on 2006-09-18 20:41:15
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