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To Factor Wouldn't Hurt

Source: AMC 8 2017 #19

November 22, 2017
AMC 8

Problem Statement

For any positive integer MM, the notation M!M! denotes the product of the integers 11 through MM. What is the largest integer nn for which 5n5^n is a factor of the sum 98!+99!+100!98!+99!+100! ? <spanclass=′latex−bold′>(A)</span>23<spanclass=′latex−bold′>(B)</span>24<spanclass=′latex−bold′>(C)</span>25<spanclass=′latex−bold′>(D)</span>26<spanclass=′latex−bold′>(E)</span>27<span class='latex-bold'>(A) </span>23\qquad<span class='latex-bold'>(B) </span>24\qquad<span class='latex-bold'>(C) </span>25\qquad<span class='latex-bold'>(D) </span>26\qquad<span class='latex-bold'>(E) </span>27
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