What is the highest possible power of 2 separating 100!

What is the highest possible power of 2 separating 100!

This is what I have until now:

50 multiples of 2

25 multiples of 4

12 multiples of 8

6 multiples of 16

3 multiples of 32

1 multiple of 64

EDIT: offering a highest possible power of 2 ^ 97

am I missing out on anything below?

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2019-05-18 21:36:30
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Answers: 2

Your checklist of multiples is proper. Yet after that the total amount is 97, not 2 ^ 97. Yet excellent to see some job.

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2019-05-21 06:00:18
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You are not missing out on anything. Making use of WolframAlpha to variable 100! right into tops, we get the solution: 2 ^ 97 × 3 ^ 48 × 5 ^ 24 × 7 ^ 16 × 11 ^ 9 × 13 ^ 7 × 17 ^ 5 × 19 ^ 5 × 23 ^ 4 × 29 ^ 3 × 31 ^ 3 × 37 ^ 2 × 41 ^ 2 × 43 ^ 2 × 47 ^ 2 × 53 × 59 × 61 × 67 × 71 × 73 × 79 × 83 × 89 × 97 (239 variables, 25 distinctive)

consequently, the highest possible power of 2 that separates 100! is 2 ^ 97.

100!/ 2 ^ 97 = 588971222367687651371627846346807888288472382883312574253249804256440585603406374176100610302040933304083276457607746124267578125

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2019-05-21 04:39:47
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