If m = 3^n, what is the greatest value of n for which m is a factor of 19!
Choose the correct choice from the following options:
A) 8  B) 10  C) 12  D) 14  E) 16
Solution-   Consider multiples of 25!=&gt; 3,6,9,12,15,18   Count no. of 3 in each multiple.   3=3x1-&gt;1   6=3x2-&gt;1   9=3x3-&gt;2   12=3x4-&gt;1   15=3x5-&gt;1   18=3x3x2-&gt;2   ---- count 3's =8 so answer is 8   8nswer : 8
<result>A</result>
If m = 3^n, what is the greatest value of n for which m is a factor of 19!