What is th remainder when the sum of the first 102 counting numbers is divided by 5220?

3 answers

1. You can find the sum of the first 102 counting numbers using Gauss's method, namely:
   "the sum of the first n counting numbers is n*(n+1)/2" whether n is odd or even.
   
   For n = 102, the sum is 102*103/2=10506.
   So divide 10506 by 5220 to get a quotient of 2, with a remainder of 66.
   
   Mental calculation tip:
   To multiply two numbers close to a hundred can be done in the head as follows, no paper, no calculators:
   
   Let the numbers be (100+x) and (100+y), where x and y are small numbers. Take the example of 102 and 103, then x=2, y=3.
   Start with the left most digit, which is a 1.
   The next two digits are the sum of x and y, that gives 105.
   The next two digits are the product of x and y, that gives 10506, et voilà!
   
   Try with 107*109, that should give 11663.

   Answer ID
   525185

   Created
   April 4, 2011 12:35pm UTC

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2. Forgot to divide 10506 by 2 according to Gauss's rule:
   10506/2=5253, divided by 5220 gives a quotient of 1 with 33 as a remainder, and divided by 5250 gives a quotient of 1 and 3 as a remainder.

   Answer ID
   525188

   Created
   April 4, 2011 12:39pm UTC

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   https://questions.llc/answers/525188

3. i have no clue i am tring ti find the answer

   Answer ID
   855181

   Created
   February 11, 2013 10:51pm UTC

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   URL
   https://questions.llc/answers/855181