## Largest Prime Divisor

If seven factorial or 7! = (1)(2)(3)(4)(5)(6)(7) = 5040, find the greatest prime divisor of the sum of 87! and 88!
Source: mathcontest.olemiss.edu 5/2/2011

SOLUTION
$87!+88!=87!+88\left (87!\right )$
$=87!\left (1+88\right )$
$=87!\left (89\right )$
$=87\times 86\times \cdots\times 3\times 2\times 1\times \left (89\right )$

89 is the greatest divisor and a prime number.