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# Factor this

## Question

n! = 1 405 006 117 752 879 898 543 142 606 244 511 569 936 384 000 000 000
What is n?

3 divides n

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42

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SP got there first. Can either of you convince the skeptics?

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On one level, that number can be shown to be between one of the numbers 40! and 44!, inclusive.

The number in the puzzle written out ends in nine zeroes, so it has exactly none factors of 10.

Then it has exactly nine factors of 5. Start listing consecutive multiples of 5, beginning with 5,

and end until you get to a multiple that contains a cumulative ninth factor of 5:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...

5, 2*5, 3*5, 4*5, 5*5, 6*5, 7*5, 8*5 ====> Stop.

If you have gone to 45 inclusive, you have gone too far, because that will provide a tenth factor of 5.

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