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?

(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