what is the highest power of 3 which divides 99999!

The number 99999! is the product of all the integers between 1 and 99999. How many of those numbers are multiples of 3? How many are multiples of 9? Of 27?

Every 3 multiple of 3 you have a multiple of 3^2. Every 3 multiple of 3^2, we have a multiple of 3^3, and so on.

So, divide by 3, and the quotient again, and again, disregarding the remainders if they are not 0

Then add all the quotients you go.

99999/3 = 33333 multiples pf 3

33333/3 = 11111 multiples of 3^2

11111/3 ~ 3703 multiples of 3^3

Etc

Then you add 33333+ 11111 + 3703 + ...

So, divide by 3, and the quotient again, and again, disregarding the remainders if they are not 0

Then add all the quotients you go.

99999/3 = 33333 multiples pf 3

33333/3 = 11111 multiples of 3^2

11111/3 ~ 3703 multiples of 3^3

Etc

Then you add 33333+ 11111 + 3703 + ...

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