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Math Help - Factorials

  1. #1
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    Factorials

    what is the largest two-digit prime factor of 200! divided by (100! 100!)
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  2. #2
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    you have to cancel this one down, not sure if I can get the answer but I can kick it off for you....

    \frac{200!}{100!\times 100!}

    \frac{200\times 199\times 198 \times \cdots101 \times 100!}{100!\times 100!}

    100! will cancel

    \frac{200\times 199\times 198 \times \cdots 101 }{100!}

    expanding the bottom

    \frac{200\times 199\times 198 \times \cdots 101 }{100\times 99\times 98 \times \cdots 1 }

    Now first 1st term of 2 should cancel on the bottom

    \frac{2\times 199\times 2 \times \cdots 101 }{ 99\times 97 \times \cdots 1 }

    There is 50 of them

    \frac{2^{50} \times 199\times 197 \times \cdots 101 }{ 99\times 97 \times \cdots 1 }

    leaving the bottom in the form

    \frac{2^{50} \times 199\times 197 \times \cdots 101 }{ 99!! }

    not sure where to go from here...
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