Answer:
14
Explanation:
You want the largest n such that 3^n is a divisor of 30!.
Factors
The factorial is the product of all the positive integers less than or equal to 30. The number of times 3 is a factor will be the total of the number of times 3 is a factor of the integers 1–30.
30/3 = 10 integers have at least one factor of 3
10/3 = 3 integers have at least 2 factors of 3
3/3 = 1 integer has 3 factors of 3
There are a total of 10+3+1 = 14 factors of 3 in the integers 1–30.
The largest value of n is 14.
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Additional comment
The attachment shows the prime factorization of 30!. As we computed, the power of 3 is 3^14.
<95141404393>