Question:
Maximum value n such that (66)! is divisible by 3n
Maximum value n such that (66)! is divisible by 3n
Updated On: Mar 27, 2026
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Solution and Explanation
The correct answer is : 31
\(\because\) 3 sis prime number,
\([\frac{66}{3}]+[\frac{66}{3^2}]+[\frac{66}{3^3}]+[\frac{66}{3^4}]+........\)
\(\Rightarrow\) 22+7+2+0+………
= 31
\((66)!=(3)^{31}........\)
maximum value of n=31
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
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Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
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