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Divisibility of a Factorial

Source:

January 14, 2009
factorial

Problem Statement

For how many positive integers n n less than or equal to 24 24 is n! n! evenly divisible by 1 \plus{} 2 \plus{} \dots \plus{} n? <spanclass=′latex−bold′>(A)</span> 8<spanclass=′latex−bold′>(B)</span> 12<spanclass=′latex−bold′>(C)</span> 16<spanclass=′latex−bold′>(D)</span> 17<spanclass=′latex−bold′>(E)</span> 21 <span class='latex-bold'>(A)</span>\ 8\qquad <span class='latex-bold'>(B)</span>\ 12\qquad <span class='latex-bold'>(C)</span>\ 16\qquad <span class='latex-bold'>(D)</span>\ 17\qquad <span class='latex-bold'>(E)</span>\ 21
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