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Question


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


Options:
A .   31
B .   15
C .   32
D .   33
E .   ¾
Answer: Option A
:
A

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=35×5.


Required answer will be the highest power of 35 in 315!


(No need to find to find the highest power of 5 in 315! as that will always be more than that of 35)


To find out highest power of 35, 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 35 in 315! = 31 (highest power of 5 we will get is 77)


Required answer is 31.



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