Problem #125

Factorial Fine Factorisations
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:
  • 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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