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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