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.

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(52908) (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   =  = 16, while the number of terms is 31.

Thanks for this entertainment problem !

RELATED QUESTIONS
E8-5 Hachey Company has accounts receivable of $95,100 at March 31, 2007. An analysis of (answered by solver91311)

Find the greatest positive prime factor of 2^20 -... (answered by Alan3354)

Find the approximate and exact number of day between the given dates: 1. January 10 to (answered by Alan3354)

Presented below are selected transactions of Menge Company. Menge sells in large... (answered by MathTherapy)

A prime number is a number that is evenly divided only by 1 and itself. The prime numbers (answered by ikleyn)

Find the Product of 62 and 31.... (answered by checkley71)

The following aged accounts receivable schedule was prepared for Dulax paints at the end... (answered by ikleyn)

The sum of three times a number and 11 is equal to that number plus... (answered by y6n3o9p4)

The sum of three times a number and 11 is equal to that number plus... (answered by geetha_rama)