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Factorial Remainder (Posted on 2011-09-02) Difficulty: 3 of 5
Determine the remainder when 98! is divided by 101

*** For an extra challenge, solve this problem without using a computer program.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution Comment 9 of 9 |

According to Wilson's Thoerem,

100! mod 101 = 100

=> 99! mod 101 = 1

=> (98! * 99) mod 101 = 1

=> 98! mod 101 = (1/99) mod 101

=> 98! mod 101 = (-1/2) mod 101

=> 98! mod 101 = ((101-1)/2) mod 101

=> 98! mod 101 = 50 mod 101

So, remainder is 50 when 98! is divided by 101


  Posted by Praneeth on 2011-09-04 12:07:43
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