Doubt in Legendre Formula

#1

Hi, I did not understand how find x while a is not prime number. Can you give some other hint .

#2

if a is not a prime number, then you can write a in term of its prime factors.
say a = 2^p x 3^q x 5^r… so on (^ denotes power function)
now a^t = 2^pt x 3^qt x 5^rt…so on
n! = 2^x1 x 3^x2 x 5^x3…

then you need pt<=x1, qt<=x2 and rt<=x3
t is min(x1/p,x2/q,x3/r)

thanks

#3

I hope I’ve cleared your doubt. I ask you to please rate your experience here
Your feedback is very important. It helps us improve our platform and hence provide you
the learning experience you deserve.

On the off chance, you still have some questions or not find the answers satisfactory, you may reopen
the doubt.