Pre RMO 2018-19(IOQM) question 1 book volume

 Pre RMO 2018-19(IOQM) question 1:


1. A book is published in three volumes, the pages being numbered from 1 onwards. The page numbers are continued from the first volume to the second volume to the third. The number of pages in the second volume is 50 more than that in the first volume, and the number of pages in the third volume is one and a half times that in the second. The sum of the page numbers on the first pages of the three volumes is 1709. If n is the last page number, what is the largest prime factor of n?

Prerequisites:
1. Divisibility by 11.

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