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Bold Minimum (Posted on 2009-12-12) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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re(2): solution Comment 4 of 4 |
(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

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