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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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re: thoughts on part B | Comment 3 of 7 |
(In reply to thoughts on part B by Charlie)

Charlie,

Can't we also combine a 2 and a 3 to utilize 5th powers in the same way you've done with two 3's for 8th powers and three 2's for 7th powers?

For example, 
2,327,925,600 = 2^5 * 3^2 * 5^2 * 7 * 11 * 13 * 17 * 19
1728 = 6 * 3 * 3 * 2 * 2 * 2 * 2 * 2

In base 12, that gives us a new low of: 54B,74B,200 (haven't found any lower so far)

  Posted by Justin on 2010-10-11 15:05:07
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