A positive integer X is defined as a bold number if precisely 8 of its distinct divisors sum to 3240. The total number of divisors of X may or may not be equal to 8.

Determine the minimum positive bold number.

(In reply to re: solution by Kenny M)

Much of my figuring was done with brute force, yet here is a little of the analysis:

As each number must be distinct, we can first find the least common denominator for the first 8 fractions:
1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, and 1/9

2,3,(2*2),5,(2*3),7,(2*2*2),(3*3) ::: 2³ * 3² * 5 * 7 = 2520

With 2520 as the denominator for the 8 distinct divisors, this gives the numerator for 1/2 as 1260.

Edited on December 14, 2009, 1:46 am

Posted by Dej Mar on 2009-12-13 17:01:43