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A 1001 Problem (Posted on 2007-02-05) Difficulty: 2 of 5
Determine the quotient and the remainder when a positive integer N constituted entirely by 1001 sevens is divided by 1001.

  Submitted by K Sengupta    
Rating: 3.2500 (4 votes)
Solution: (Hide)
The number 777,777 is precisely divisible by 1001 giving the quotient 777.

Hence, the number 777…700000 (996 sevens and 5 zeroes) yields upon division by 1001, a quotient of: 777000777000…77700000( the grouping 777,000 repeated 166 times).

Moreover, the number 77,777 yields a quotient of 77 and a remainder of 700 uopn division by 1001.

Consequently, the quotient obtained by dividing N with 1001 is equal to:

77700077700077 . . . 77700077 (containing 998 digits with the grouping 777,000 repeated 166 times), and; there is the remainder of 700.
......................................

Also, refer to the solution provided by Leming in this location.

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SolutionSolutionLeming2007-02-05 10:09:07
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