Difference between revisions of "1983 AIME Problems/Problem 8"

Revision as of 20:51, 1 February 2007

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)
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All AIME Problems and Solutions

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-* [[1983 AIME Problems/Problem 7|Previous Problem]]
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+{{AIME box|year=1983|num-b=7|num-a=9}}
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