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# Factoring Factorials

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Age 11 to 14

Challenge Level

Find the highest power of 11 that will divide 1000! exactly.

[Factorial 1000, written 1000!, is the product of the first 1000 whole numbers 1 x 2 x 3 x ... x 1000]

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?