Correct option is C
Solution:
We need to find how many factors of 3 are in 30! (1 × 2 × 3 × ... × 30).
To count the factors of 3:
· The number of multiples of 3 is 30 ÷ 3 = 10.
· The number of multiples of 9 (which contribute an additional factor of 3) is 30 ÷ 9 = 3.
· The number of multiples of 27 (which contribute yet another factor of 3) is 30 ÷ 27 = 1.
So, the total number of factors of 3 in 30! is:
10 (from multiples of 3) + 3 (from multiples of 9) + 1 (from multiples of 27) = 14.
Therefore, the largest power of 3 that divides 30! is 314.
Final Answer:
(c) 314.
