Suppose the number of pages is the First Volume is **t**.

It’s first page is numbered 1. Then the second volume has** t+50** pages.

Its first page is numbered **t+1**. Finally, the third volume has \( \frac{3}{2} \times ( t + 50) \) pages. Its first page is (t + t + 50 + 1 =) 2t + 51.

Sum of the page numbers of first pages of three volumes is:

1 + t +1 + 2t + 51 = 3t + 51. 3t + 51 = 1709 This implies t= 552

The total number of pages in three volumes is

\( t + t + 50 + \frac{3}{2} \times (t+50) \\ = \frac {4t + 100 + 3t + 150}{2} \\ = \frac { 7 \times 552 + 250}{2} \\ = 2057 = 11^2 \times 17 \).

Hence the greatest prime factor is 17.

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