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Prime Factor (Posted on 2006-05-12) Difficulty: 4 of 5
Determine the largest 3 - digit prime factor of 2000 C 1000.

n C r denotes the number of combinations of n things taking r at a time.

No Solution Yet Submitted by Ravi Raja    
Rating: 2.5000 (2 votes)

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Solution Answer Comment 8 of 8 |
2000C1000 = 2000*1999*.......*1001/1000! 
=> 2000C1000 = 2^(500) {odds from 1001 to 2000}/500!
As odds cannot be multiple of 2, next possibility is 3.
Maximum prime between 500 and 667 is the largest 3-digit
prime factor of 2000 C 1000
The required number is 661.

  Posted by Praneeth on 2008-02-05 03:12:14
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