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"In mathematics, Kummer's theorem on binomial coeffients gives the highest power of a prime number p dividing a binomial coefficient. In particular, it asserts that given integers n ≥ m ≥ 0 and a prime number p, the maximum integer k such that pk divides the binomial coefficient \tbinom n m is equal to the number of carries when m is added to n − m in base p."
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Binomial Coefficients Revenge
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Probably something in this paper tells how to do this http://www.dms.umontreal.ca/~andrew/PDF/BinCoeff.pdf http://en.wikipedia.org/wiki/Kummer%27s_theorem
"In mathematics, Kummer's theorem on binomial coeffients gives the highest power of a prime number p dividing a binomial coefficient. In particular, it asserts that given integers n ≥ m ≥ 0 and a prime number p, the maximum integer k such that pk divides the binomial coefficient \tbinom n m is equal to the number of carries when m is added to n − m in base p."