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

Line 1: Line 1:
 
== Problem ==
 
== Problem ==
What is the largest 2-digit prime factor of the integer <math>\binom{200}{100}</math>?
+
What is the largest 2-digit prime factor of the integer <math>{200\choose 100}</math>?
  
 
== Solution ==
 
== Solution ==

Revision as of 23:06, 23 July 2006

Problem

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

Solution

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.


See also