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Gross Division (Posted on 2006-02-20) Difficulty: 3 of 5
Find the smallest positive integer n such that n has exactly 144 distinct positive divisors and there are 10 consecutive integers among them (Note: 1 and n are both divisors of n)

See The Solution Submitted by goFish    
Rating: 3.8000 (5 votes)

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re: improved further | Comment 5 of 14 |
(In reply to Slightly improved by Tristan)

We can do better.

I started with another set of 10 consecutive integers with the idea that the integer 12, with its multiple factors would be useful in reducing the final result:


The factors required for these divisors:

which has 96 divisors

Adding another factor of 5 gives us 144 divisors.

The resulting number is 23*32*52*7*11 = 138,600.

Perhaps a better solution exists, even yet?

  Posted by Mindrod on 2006-02-20 14:24:52
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