$\frac{53!}{3^{n}}$ is an integer. Find the highest possible value of n for this to be true.

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Solution

The correct option is C 23
No of 3's in $53! = [\frac{53}{3}] + [\frac{53}{9}] + [\frac{53}{27}] =$ 17 + 5 + 1 = 23.
Option (c) is correct.

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(IIT JEE 2012)

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53!3n is an integer. Find the highest possible value of n for this to be true.

The correct option is C 23No of 3's in 53!=[533]+[539]+[5327]= 17 + 5 + 1 = 23. Option (c) is correct.

$\frac{53!}{3^{n}}$ is an integer. Find the highest possible value of n for this to be true.

The correct option is C 23
No of 3's in $53! = [\frac{53}{3}] + [\frac{53}{9}] + [\frac{53}{27}] =$ 17 + 5 + 1 = 23.
Option (c) is correct.