If m = 3^n, what is the greatest value of n for which m is a factor of 31!
Pick one:
A) 8	B) 10	C) 12	D) 14	E) 16
Solution-   Consider multiples of 25!=&gt; 3,6,9,12,15,18,21,24,27,30   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   21=3x7-&gt;1   24=3x8-&gt;1   27=3x3x3-&gt;3   30=3x10-&gt;1   ---- count 3's =14 so answer is 14   Answer : 14
<result>D</result>
If m = 3^n, what is the greatest value of n for which m is a factor of 31!