1983 AIME Problems/Problem 8

Problem

What is the largest 2-digit prime factor of the integer ${200\choose 100}$ ?

Expanding the binomial coefficient, we get ${200 \choose 100}=\frac{200!}{100!100!}$ .

Therefore, our two digit prime $p$ must satisfy $3p<200$ . The largest such prime is $61$ , which is our answer.

1983 AIME (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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