If m = 3^n, what is the greatest value of n for which m is a factor of 22! Pick one.
A) 8
B) 10
C) 9
D) 14
E) 16

Rationale: "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 , 18,21 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 - - - - count 3 ' s = 9 so answer is 9 answer : c"
Answer: C