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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 The Same Method - just slower | Comment 3 of 8 |

661.

Not as elegant as K.S.'s but it follows that 2000!/(1000! * 1000!) is

 (2000 * 1999 * 1998 * . . . * 1001 )

     (1000 * 999 * 998 * . . . *1)

All the numbers between 1001 and 2000 that are divisible by 2 can be tossed. This leaves numbers between 1001 and 2000 that are divisible by 3 (666, 665, 664 . . .). The highest prime in this set is 661.

Edited on May 12, 2006, 12:45 pm
  Posted by Leming on 2006-05-12 12:37:31

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