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.

1260

1260 has factors 2² x 3² x 5 x 7

1260 = [2x2x3x3x5x7]
 630 = [2  x3x3x5x7]
 420 = [2x2x3  x5x7]
 315 = [    3x3x5x7]
 252 = [2x2x3x3  x7]
 210 = [2  x3  x5x7]
  90 = [2  x3x3x5  ]
  63 = [    3x3  x7]
3240

 

Edited on December 13, 2009, 4:19 pm

Posted by Dej Mar on 2009-12-12 16:50:08