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Oodles of Factors II (Posted on 2010-10-11) Difficulty: 3 of 5
A. What is the lowest base 12 positive integer that has exactly 10 (base 12) distinct positive factors?

B. Exactly 1,000 (base 12) distinct positive factors?

C. Exactly 1,000,000 (base 12) distinct positive factors?

For example, the distinct positive factors of 40 (base 12) are the base 12 numbers 1, 2, 3, 4, 6, 8, 10, 14, 20, and 40. Accordingly, 40 (base 12) has precisely A (base 12) distinct positive factors.

No Solution Yet Submitted by K Sengupta    
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Part C | Comment 5 of 7 |

running the same code as before gives the smallest value as
in base 10:
130,085,492,110,229,957,747,846,400
which factorized is
2^8*3^5*5^2*7^2*11^2*13*17*19*23*29*31*37*41*43
*47*53
and in base 12:
1,777,769,B4B,219,9B7,304,790,000

Edited on October 12, 2010, 11:55 am
  Posted by Daniel on 2010-10-11 19:45:39

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