<PRE><B>Question 989901</B>
&lt;table border=1&gt;&lt;tr&gt;&lt;th&gt;Original Statement&lt;/th&gt;&lt;th&gt;Translation&lt;/th&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;The last digit is even&lt;/td&gt;&lt;td&gt;2 is a factor&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Sum of the digits is divisible by 3&lt;/td&gt;&lt;td&gt;3 is a factor&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;The last 2 digits are divisible by 4&lt;/td&gt;&lt;td&gt;4 is a factor&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;The last digit is 0 or 5&lt;/td&gt;&lt;td&gt;5 is a factor&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;The number is divisible by 2 and 3&lt;/td&gt;&lt;td&gt;6 is a factor&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;The last 3 digits form a number divisible by 8&lt;/td&gt;&lt;td&gt;8 is a factor&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;The sum of the digits is divisible by 9&lt;/td&gt;&lt;td&gt;9 is a factor&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;The last digit is 0&lt;/td&gt;&lt;td&gt;10 is a factor&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;


In short, we know this number has the following factors: 2,3,4,5,6,8,9,10


There could be other factors or repeats of those factors above. Let&#39;s say that there is only one copy of each and only those factors are there


Multiply out all the factors: 2*3*4*5*6*8*9*10 = 518,400


So the smallest number possible is &lt;font color=&quot;red&quot;&gt;518,400&lt;/font&gt; Any other multiple of this number works as well.</PRE>