Question

When 315! is divided by ${1215}^x$, remainder=0. What is the maximum possible value for x?

• A. 31
• B. 15
• C. 32
• D. 33
• E. none of these

Answer 1

The correct option is A 31

option (a)

Highest power of a number in a factorial

Here since 1215 is composite number, prime factorize 1215 i.e $1215=3^5\ast 5$

Required answer will be the highest power of $3^5$ in 315!

( no need to find to find the highest power of 5 in 315! as that will always be more than that of $3^5$.)

To find out highest power of $3^5$, we will first find the highest power of 3 and then

divide it by 5.

Highest power of 3 in 315! = 155

Highest power of $3^5$in 315! = 31 (highest power of 5 we will get as 76 )

Required answer is 31.