1. Largest prime number

$Finding largest prime number which divide \displaystyle \binom{2000}{1000}$

$We can write \displaystyle \binom{2000}{1000} = \frac{2000!}{1000!\cdot 1000!} = \frac{1001 \cdot 1002 \cdot 1003\cdots \cdots 2000}{1000!}$

i did not understand how to solve further, please explain me

2. Re: Largest prime number

Originally Posted by juantheron
$Finding largest prime number which divide \displaystyle \binom{2000}{1000}$

$We can write \displaystyle \binom{2000}{1000} = \frac{2000!}{1000!\cdot 1000!} = \frac{1001 \cdot 1002 \cdot 1003\cdots \cdots 2000}{1000!}$

i did not understand how to solve further, please explain me
You can simplify further to
$\noindent \frac{1001 \cdot 2 \cdot 1003 \cdot 2 \cdots 1999 \cdot 2}{500!} \\ \\ =\frac{2002 \cdot 2006 \cdots 3998}{500!} \\ \\ =\frac{1001 \cdots 1999}{250! \cdot 3 \cdot \cdots 499}$

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