The highest power of 9 dividing 99 completely is

Asked by admin @ 17/08/2021 in Math viewed by 313 People

The highest power of 9 dividing 99 factorial completely is

Answered by admin @ 17/08/2021

This is the same as asking what is the highest multiple of 3 that divides 99!, divided by two and rounded down. So lets look at how many multiples of 3 there are.

First, every third number will be divisible by 3, starting with 3. This gives 33 3s.

Next, every third multiple of 3 is divisible twice, so we'll count them extra. Starting from 9, this gives 11 3s.

Next, every third multiple of those will be divisible 3 times, so they get another count on top. These are 27, 54, and 81, or 3 extra 3s.

Finally, 81 actually has 4 multiples of 3, so we'll add it in one last time for a grand total of 33+11+3+1=48 3s, or 24 multiples of 9. Thus 9^24 will divide 99! evenly.

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Asked by admin @ 05/11/2021 in Mathematics viewed by 284 persons

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Asked by admin @ 29/10/2021 in Mathematics viewed by 239 persons

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Asked by admin @ 26/11/2021 in Mathematics viewed by 273 persons

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Asked by admin @ 26/11/2021 in Physics viewed by 331 persons

When using a Microscope's high power objective the course adjustment knob: a. Can be used throughout the focusing process. b. Can not be used with low power object c. Can …