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

Answer 1

The correct option is A 31

The question is based on highest power of a number in a factorial.

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

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 (105 + 35 + 11 + 3 + 1)

Highest power of $3^5$ in 315! = 31 (highest power of 5 we will get is 77)

Required answer is 31.