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# Powerful Factorial

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Age 11 to 14

Challenge Level

6! = 6 x 5 x 4 x 3 x 2 x 1

The highest power of 2 that divides exactly into 6! is 4.

**((6!) / (2 ^{4} ) = 45)**

What is the highest power of two that divides exactly into 100! (100 x 99 x 98 x 97 x ... x 1)?

What is the highest power of three that divides exactly into 100! ?

.......

Can you see any patterns in the calculation of the highest powers of each number that divides exactly into 100!?

Can you generalise your findings to any factorial and any number?