<PRE><B>Question 1062628</B>
&lt;pre&gt;&lt;b&gt;&lt;font size=5&gt;
 3 =     3
 6 = 2&amp;#8729;  3
 9 =     3&amp;#8729;3
12 = 2&amp;#8729;2&amp;#8729;3
15 =     3  &amp;#8729;5
18 = 2&amp;#8729;  3&amp;#8729;3

So 3&amp;#8729;6&amp;#8729;9&amp;#8729;12&amp;#8729;15&amp;#8729;18 = 2&lt;sup&gt;4&lt;/sup&gt;&amp;#8729;3&lt;sup&gt;8&lt;/sup&gt;&amp;#8729;5 

A perfect square must have an even power
of each of its prime factors.  Since we want
factors of  2&lt;sup&gt;4&lt;/sup&gt;&amp;#8729;3&lt;sup&gt;8&lt;/sup&gt;&amp;#8729;5 the exponents of
the primes must not exceed the exponents of
2,3,and 5 in 2&lt;sup&gt;4&lt;/sup&gt;&amp;#8729;3&lt;sup&gt;8&lt;/sup&gt;&amp;#8729;5. 

All factors of 3•6•9•12•15•18 are of the form

2&lt;sup&gt;x&lt;/sup&gt;&amp;#8729;3&lt;sup&gt;y&lt;/sup&gt;&amp;#8729;5&lt;sup&gt;z&lt;/sup&gt;, where x, y, and z are even integers,
[including 0].

The possible even powers of 2 are 0, 2, and 4.

Therefore there are 3 ways to choose the power of 2. 

The possible powers of 3 are 0,2,4,6 and 8.

So there are 5 ways to choose the power of 3.

The only possible power of 5 is 0.

So there is only 1 way to choose the power of 5, (as 0)

The answer would be 3 ways times 5 ways times 1 way 

= 3&amp;#8729;5&amp;#8729;1 = 15 ways.

However, since it says &quot;greater than 1&quot; we must subtract 
1 from the 15, so 

Answer = 14.

Here are all 15 factors of 3&amp;#8729;6&amp;#8729;9&amp;#8729;12*15&amp;#8729;18:

 1. 2&lt;sup&gt;0&lt;/sup&gt;3&lt;sup&gt;0&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 1 &lt;--can&#39;t use this!
 2. 2&lt;sup&gt;0&lt;/sup&gt;3&lt;sup&gt;2&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 9
 3. 2&lt;sup&gt;0&lt;/sup&gt;3&lt;sup&gt;4&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 81
 4. 2&lt;sup&gt;0&lt;/sup&gt;3&lt;sup&gt;6&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 729
 5. 2&lt;sup&gt;0&lt;/sup&gt;3&lt;sup&gt;8&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 6561
 6. 2&lt;sup&gt;2&lt;/sup&gt;3&lt;sup&gt;0&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 4
 7. 2&lt;sup&gt;2&lt;/sup&gt;3&lt;sup&gt;2&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 36
 8. 2&lt;sup&gt;2&lt;/sup&gt;3&lt;sup&gt;4&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 324
 9. 2&lt;sup&gt;2&lt;/sup&gt;3&lt;sup&gt;6&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 2916
10. 2&lt;sup&gt;2&lt;/sup&gt;3&lt;sup&gt;8&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 26244
11. 2&lt;sup&gt;4&lt;/sup&gt;3&lt;sup&gt;0&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 16
12. 2&lt;sup&gt;4&lt;/sup&gt;3&lt;sup&gt;2&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 144
13. 2&lt;sup&gt;4&lt;/sup&gt;3&lt;sup&gt;4&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 1296
14. 2&lt;sup&gt;4&lt;/sup&gt;3&lt;sup&gt;6&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 11664
15. 2&lt;sup&gt;4&lt;/sup&gt;3&lt;sup&gt;8&lt;/sup&gt;5&lt;sup&gt;0&lt;/sup&gt; = 104976

Edwin&lt;/pre&gt;&lt;/b&gt;&lt;/font&gt;

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