PrepSwift: # of Numbers in Factorials II Quiz - Question 5

Explanation video doesn’t have the solution. Please explain how to solve this question

How would you do this problem?

-k!/2^6n
-given n is 11
-k!/2^66…

You’re on the right track. So you found out that 2^{66} divides k!. Is that the largest though? What about p = 67 or p = 68? Would that work?

My understanding is p needs to be a multiple of 6. Hence, 2^72 divides k! which is the largest integer.. P=72?

Close but not there. If p = 72, what would the original answer be (i.e, for 64^n)?

oh..that would be 12 and not 11..so P will be 71?

There you go.

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Thank you so much