Factorial Fine Factorisations
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Public  06/09/14  8xp  Math  84.6% 
A factorisation of N in factors is fine if each factor contains only 1 prime number:
6! = 720 possesses 10 fine factorisations:
How many fine factorisations are there for 10000!
Give the digital sum of this large number.
[My timing : 1 sec]
6! = 720 possesses 10 fine factorisations:
 5 9 16
 3 3 5 16
 2 5 8 9
 2 3 3 5 8
 4 4 5 9
 3 3 4 4 5
 2 2 4 5 9
 2 2 3 3 4 5
 2 2 2 2 5 9
 2 2 2 2 3 3 5
How many fine factorisations are there for 10000!
Give the digital sum of this large number.
[My timing : 1 sec]
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