Question
A number n! is written in base 6 and base 8 notation. Its base 6 representation ends with 10 zeroes. Its base 8 representation ends with 7 zeroes. Find the smallest n that satisfies these conditions. Also find the number of values of n that will satisfy these conditions
CAT 2021
Solution
Correct option is
(C)
Explanatory Answer
According to ques , the number is a multiple of
if n! is a multiple of , it has to be a multiple of
the smallest factorial should be 24! , so , when n= 24, 25 or 26 , n! will be multiple of (not
)
similarly ,we have to find n! such that it is a multiple of
hence the smallest n from 24 , 25 , 0r 26 , will be 24 .
hence C is the correct option , "24 , 3"
