The product 1 X 2 X 3 X 4 X ... X 2011 X 2012 = (18^a X b )where a and b are whole numbers. What is the largest value of a?

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I think I'll make the above question clearer: The product \[1\times2\times3\times4\times...2011\times2012=18^{a} \times b \] where a and b are whole numbers. What is the largest value of a?

There are \[\left \lfloor {2012 \over 18} \right \rfloor =111\] multiples of 18 less than 200. Taking into account 2*9 and 3*6, I'd say that a can be at most 113.

18^2 contributes an additional 18, so that becomes 114.

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