Question on factorial.
Question on factorial.
what is the highest power of 3 which divides 99999!
Re: Question on factorial.
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?
Re: Question on factorial.
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 + ...