SOLUTION: March has 31 days. Let S equal the sum of the dates 1 to 31. Find the greatest prime factor of S. Explain your solution. Thank you.

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Question 1137370: March has 31 days. Let S equal the sum of the dates 1 to 31. Find the
greatest prime factor of S. Explain your solution. Thank you.
Answer by ikleyn(52905) About Me  (Show Source):
You can put this solution on YOUR website!
.
The greatest prime factor of this sum  S  is 31.



It becomes OBVIOUS if you recall the formula for the sum of an arithmetic progression.


This sum is the product of the arithmetic mean of the first and the last terms by the number of terms.


The mean arithmetic in this case is  %281+%2B+31%29%2F2 = 32%2F2 = 16, while the number of terms is 31.

Thanks for this entertainment problem !