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I've seen a "2.303" term multiplied to $R$ in Van't Hoff equation several times.
Here is one example:
http://en.wikipedia.org/wiki/Van_%27t_Hoff_equation#Error_propagation
$$\Delta H^\circ=2.303R\frac{\log K_1-\log K_2}{\frac1{T_2}-\frac1{T_1}}$$
What is this number and where does it come from?
It is the multiplier used when converting the equation to use a base 10 log instead of a natural log.
It comes out to be the natural log of 10.
To elaborate on Burak's answer, which states that 2.303 is the multiplier, the correct converison is:
$$\ln(x) = 2.303\cdot\log_{10}(x)$$
Or as a divisor to convert the natural logarithm to a base 10 log: $$\log_{10}(x) = \frac{\ln(x)}{2.303}$$
